WEBVTT

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Thank you all for attending the
Earthquake Science Center Weekly

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Seminar Series.

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If you are new, welcome.

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00:00:13.063 --> 00:00:13.810
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Seminars are recorded.

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Mostly all talks are posted on
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Attendees please mute your mics
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the Q&A session at the end
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00:00:32.120 --> 00:00:35.567
Or you can submit your questions
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00:00:35.567 --> 00:00:38.805
to turn on your camera and
ask your question during the

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00:00:38.805 --> 00:00:39.640
Q&A session.

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Please note that we have an
All Hands scheduled tomorrow at

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11:00 AM, so keep your eyes
peeled for announcements

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00:00:49.520 --> 00:00:51.250
regarding that meeting.

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You are also invited to attend
the 2024 3-day USGS Northern

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California Earthquake Hazards
Workshop on January 30th through

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February 1st.

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In lieu of posters this year,
and if you're interested, we are

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inviting attendees to present
short talks 5 minutes or less,

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highlighting progress related to
Northern California earthquake

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hazards.

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The workshop is free and open to
all who are interested in better

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defining earthquake hazards and
risk in Northern California.

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Register today and please see
the link in the chat.

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Please note that the workshop is
still accepting Thunder Talks,

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which are those short 5 minute
talks until Tuesday, January

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00:01:31.117 --> 00:01:31.430
16th.

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Next week there will also be a
watch party at Moffett Field and

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Yosemite Conference room for the
conference.

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So if you're around, please join
us.

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Please also be sure to submit
your SSA abstracts to the

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conference today.

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Today's the deadline which
should have been approved for

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submission by the Science Center
at this point.

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So if you got approval and
you are waiting on your

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submission, please do so by the
end of today.

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A gentle reminder to be a mentor
and host an ESC intern this

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summer.

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The deadline is Friday, January
12th, 2024.

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There's also a link there which
Susan will post in the chat and

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please reach out if you have
questions.

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And finally, Not Ready for Prime
Time is back on in the new year

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from 3:00 to 4:00 PM in the
Yosemite Conference room.

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Please join us. So with that I
will turn it over to Ben and he

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will introduce our speaker
today.

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Alright.

bda32352-a5ee-4f54-a17e-dc796256864d/574-0
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Hi everybody! You can hear me?

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Great.

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All good.

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So like being asked to
introduce Sarah is like I was

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reflecting on this.

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It's like it must be what it
feels like to be asked to

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introduce like the notorious RBG
or Venus Williams or

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something like that, like she's
had such an impact on the Center

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and the field that she almost
doesn't need an introduction,

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but it's also fun to talk about
Sarah a little bit.

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She got her undergrad at Cal and
PhD at Cal Tech doing extensibly

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geodesy, but also really making
some fundamental contributions

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with Bayesian inversion, which
she's going to come back to in

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this talk and then she did
a Mendenhall with us.

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We were lucky enough to hire
her.

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She's extremely awarded winning
the PK Presidential Award for

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Young Investigators, which is, I
think the highest honor that

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young investigators can win 
at the Survey.

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So just briefly, as a scientist,
her career and her contributions

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have been extremely broad and
impressive.

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She's written really seminal
work in Earthquake.

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Early Warning that I think many
people know about and the

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whole community has paid
attention to and really sort of

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changed the course of that
community.

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She's also written really
fundamental work about inverse

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[noise]

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processes.

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[noise]

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And and then she's also made all
sorts of contributions, studying

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ground motion associated with a
little earthquakes, for

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instance.

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All really interesting stuff,
all really broad.

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And then also if you think about
her as a colleague or her

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contribution to the Center,
she's got leadership in terms

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of the High Performance
Computing with NASA that she's

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 led and then also taking over
the mantle of the NorCal

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Workshop, which we heard Curtis
introduced, which is really

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important 

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community aspect that the
the Center has done for the

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years and she took over from the
beloved Jack Boatwright doing

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that?

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So I 

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think the thing that I'll
leave you with that I thought

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about is like talking with Sarah
and I think Jack Boatwright

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would appreciate this analogy
because he's an old Deadhead,

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was an old Deadhead.

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Talking with Sarah,

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I'm like an intellectual
project or anything;

bda32352-a5ee-4f54-a17e-dc796256864d/1042-0
00:05:03.780 --> 00:05:09.041
 It's kind of like the best of
the old Jerry Garcia solos that

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You had no

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idea where they're
going to go, but they went to

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amazing places and they always
came back home to the point and

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the crowd roared.

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So with that, Sarah is going to
talk today about extremely

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efficient Bayesian inversion.

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I think it's going to be really
fun talk.

bda32352-a5ee-4f54-a17e-dc796256864d/1112-0
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Ah, thank you so much, Ben.

bda32352-a5ee-4f54-a17e-dc796256864d/1135-0
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That is such a sweet
introduction and I am going to

bda32352-a5ee-4f54-a17e-dc796256864d/1135-1
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repay you with such a
complicated and unhappy talk.

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00:05:35.180 --> 00:05:39.536
So thank you everyone for coming
out. A little bit of a note about

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the talk.

bda32352-a5ee-4f54-a17e-dc796256864d/1169-0
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I'm gonna talk a lot about
finite fault source models.

bda32352-a5ee-4f54-a17e-dc796256864d/1176-0
00:05:44.040 --> 00:05:45.060
I can't help it.

bda32352-a5ee-4f54-a17e-dc796256864d/1182-0
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It's what I study.

bda32352-a5ee-4f54-a17e-dc796256864d/1210-0
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It's the words that come out of
my mouth, but actually there's

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nothing in this talk that's
about earthquake models.

bda32352-a5ee-4f54-a17e-dc796256864d/1249-0
00:05:51.740 --> 00:05:55.793
It's all just about inverse
theory, so when I say earthquake

bda32352-a5ee-4f54-a17e-dc796256864d/1249-1
00:05:55.793 --> 00:05:59.913
rupture model, please hear, you
know earthquake statistics or

bda32352-a5ee-4f54-a17e-dc796256864d/1249-2
00:05:59.913 --> 00:06:03.500
earthquake dynamics or whatever
it is that you study.

bda32352-a5ee-4f54-a17e-dc796256864d/1272-0
00:06:04.800 --> 00:06:08.510
OK. So this is a talk about
friendship and I wanna talk

bda32352-a5ee-4f54-a17e-dc796256864d/1272-1
00:06:08.510 --> 00:06:12.020
especially about four friends in
alphabetical order,

bda32352-a5ee-4f54-a17e-dc796256864d/1283-0
00:06:12.230 --> 00:06:18.580
those would be then Jess, Josie,
and Math.

bda32352-a5ee-4f54-a17e-dc796256864d/1293-0
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And I know that math isn't for
everyone.

bda32352-a5ee-4f54-a17e-dc796256864d/1326-0
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Math can be very divisive, and
if math isn't for you, like

bda32352-a5ee-4f54-a17e-dc796256864d/1326-1
00:06:24.169 --> 00:06:27.036
maybe this talk isn't for you
and you just want to head out,

bda32352-a5ee-4f54-a17e-dc796256864d/1326-2
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that's fine.

bda32352-a5ee-4f54-a17e-dc796256864d/1330-0
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You won't hurt my feelings.

bda32352-a5ee-4f54-a17e-dc796256864d/1343-0
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You might hurt Math's feelings,
but I'm gonna be OK.

bda32352-a5ee-4f54-a17e-dc796256864d/1393-0
00:06:34.190 --> 00:06:37.291
OK. So, once Upon a time I went
to grad school and we wanted to

bda32352-a5ee-4f54-a17e-dc796256864d/1393-1
00:06:37.291 --> 00:06:40.096
make earthquake rupture models
to learn about earthquake

bda32352-a5ee-4f54-a17e-dc796256864d/1393-2
00:06:40.096 --> 00:06:42.950
rupture physics course that
requires actually knowing the

bda32352-a5ee-4f54-a17e-dc796256864d/1393-3
00:06:42.950 --> 00:06:45.460
earthquake rupture, which you
don't get to absorb.

bda32352-a5ee-4f54-a17e-dc796256864d/1413-0
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So interactive yourself an
invoice problem and the invoice

bda32352-a5ee-4f54-a17e-dc796256864d/1413-1
00:06:48.340 --> 00:06:49.750
problem is tailorable, right?

bda32352-a5ee-4f54-a17e-dc796256864d/1420-0
00:06:49.760 --> 00:06:51.430
There are multiple models that
fit the data.

bda32352-a5ee-4f54-a17e-dc796256864d/1440-0
00:06:53.280 --> 00:06:56.066
Small changes in the model
design lead to big changes in

bda32352-a5ee-4f54-a17e-dc796256864d/1440-1
00:06:56.066 --> 00:06:58.070
the informed rupture right on
the right.

bda32352-a5ee-4f54-a17e-dc796256864d/1457-0
00:06:58.080 --> 00:07:03.160
I'm showing 4 published models
from the 1992 Landos earthquake.

bda32352-a5ee-4f54-a17e-dc796256864d/1460-0
00:07:04.060 --> 00:07:05.700
Umm it?

bda32352-a5ee-4f54-a17e-dc796256864d/1465-0
00:07:07.700 --> 00:07:09.380
That's interesting.

bda32352-a5ee-4f54-a17e-dc796256864d/1475-0
00:07:12.550 --> 00:07:13.670
I sledge just jumped.

bda32352-a5ee-4f54-a17e-dc796256864d/1487-0
00:07:17.830 --> 00:07:19.800
And a lot of what you see is
smoothing.

bda32352-a5ee-4f54-a17e-dc796256864d/1492-0
00:07:19.810 --> 00:07:22.480
It is not actually.

bda32352-a5ee-4f54-a17e-dc796256864d/1497-0
00:07:25.140 --> 00:07:25.930
The sauce itself.

bda32352-a5ee-4f54-a17e-dc796256864d/1521-0
00:07:28.890 --> 00:07:32.390
So what we need is the ensemble
of all plausible source models

bda32352-a5ee-4f54-a17e-dc796256864d/1521-1
00:07:32.390 --> 00:07:35.000
constrained only by physics, not
by smoothing.

bda32352-a5ee-4f54-a17e-dc796256864d/1528-0
00:07:35.010 --> 00:07:36.360
But we need this Bayesian
inversion.

bda32352-a5ee-4f54-a17e-dc796256864d/1549-0
00:07:40.750 --> 00:07:45.955
And so, umm, you let's take a
moment to actually understand

bda32352-a5ee-4f54-a17e-dc796256864d/1549-1
00:07:45.955 --> 00:07:47.950
how basin abortion was.

bda32352-a5ee-4f54-a17e-dc796256864d/1583-0
00:07:47.960 --> 00:07:50.537
So you might be familiar with
like thinking of inversions is D

bda32352-a5ee-4f54-a17e-dc796256864d/1583-1
00:07:50.537 --> 00:07:53.032
= g * M But the first thing is
in Bayesian analysis we don't

bda32352-a5ee-4f54-a17e-dc796256864d/1583-2
00:07:53.032 --> 00:07:53.890
use EM, we use Theta.

bda32352-a5ee-4f54-a17e-dc796256864d/1598-0
00:07:55.000 --> 00:07:59.522
And we write the model as the
solution is a posterior

bda32352-a5ee-4f54-a17e-dc796256864d/1598-1
00:07:59.522 --> 00:08:00.610
distribution.

bda32352-a5ee-4f54-a17e-dc796256864d/1623-0
00:08:00.620 --> 00:08:04.144
It's a PDF that describes the
relative plausibility of all

bda32352-a5ee-4f54-a17e-dc796256864d/1623-1
00:08:04.144 --> 00:08:07.010
possible values of your model
parameters Theta.

bda32352-a5ee-4f54-a17e-dc796256864d/1659-0
00:08:07.080 --> 00:08:10.732
Given your observations D and
basically what it says that

bda32352-a5ee-4f54-a17e-dc796256864d/1659-1
00:08:10.732 --> 00:08:14.698
that's equal to the likelihood,
which is simply the the misfit

bda32352-a5ee-4f54-a17e-dc796256864d/1659-2
00:08:14.698 --> 00:08:18.098
between your data and the
predictions from your model

bda32352-a5ee-4f54-a17e-dc796256864d/1659-3
00:08:18.098 --> 00:08:18.790
parameters.

bda32352-a5ee-4f54-a17e-dc796256864d/1676-0
00:08:19.020 --> 00:08:21.626
Your prior distribution, which
is your constraints and what you

bda32352-a5ee-4f54-a17e-dc796256864d/1676-1
00:08:21.626 --> 00:08:23.050
think the model framers should
be.

bda32352-a5ee-4f54-a17e-dc796256864d/1716-0
00:08:23.100 --> 00:08:25.529
So for example, in finite
thought models, we typically

bda32352-a5ee-4f54-a17e-dc796256864d/1716-1
00:08:25.529 --> 00:08:28.002
want to put a backflip
constraint on all faults so that

bda32352-a5ee-4f54-a17e-dc796256864d/1716-2
00:08:28.002 --> 00:08:30.696
they don't slip backwards and
then the denominator is P of D

bda32352-a5ee-4f54-a17e-dc796256864d/1716-3
00:08:30.696 --> 00:08:32.330
it's called the marginal
likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/1725-0
00:08:33.390 --> 00:08:34.230
Looks like a function.

bda32352-a5ee-4f54-a17e-dc796256864d/1747-0
00:08:34.450 --> 00:08:40.538
Actually a scalable number and
if you want to know umm what

bda32352-a5ee-4f54-a17e-dc796256864d/1747-1
00:08:40.538 --> 00:08:42.060
that is, it is.

bda32352-a5ee-4f54-a17e-dc796256864d/1755-0
00:08:42.250 --> 00:08:44.460
And easier to write you.

bda32352-a5ee-4f54-a17e-dc796256864d/1772-0
00:08:44.510 --> 00:08:46.780
You first have to write it the
way the ******** bayesians do.

bda32352-a5ee-4f54-a17e-dc796256864d/1787-0
00:08:46.830 --> 00:08:49.987
The ******** bayesians put
another variable in this they

bda32352-a5ee-4f54-a17e-dc796256864d/1787-1
00:08:49.987 --> 00:08:51.980
use fancy script M for model
class.

bda32352-a5ee-4f54-a17e-dc796256864d/1801-0
00:08:51.990 --> 00:08:55.890
It's all the things you had to
assume to design your model,

bda32352-a5ee-4f54-a17e-dc796256864d/1801-1
00:08:55.890 --> 00:08:56.280
right?

bda32352-a5ee-4f54-a17e-dc796256864d/1814-0
00:08:56.290 --> 00:08:58.600
It's things like for finite Fort
models.

bda32352-a5ee-4f54-a17e-dc796256864d/1873-0
00:08:58.750 --> 00:09:01.760
It's the geometry of your
thought, the discretization of

bda32352-a5ee-4f54-a17e-dc796256864d/1873-1
00:09:01.760 --> 00:09:04.716
your fault, the elastic
structure in which you embedded

bda32352-a5ee-4f54-a17e-dc796256864d/1873-2
00:09:04.716 --> 00:09:08.095
your fault, the location of your
earthquake, all these sorts of

bda32352-a5ee-4f54-a17e-dc796256864d/1873-3
00:09:08.095 --> 00:09:11.421
things, and so you can think of
the denominator PFD given M as

bda32352-a5ee-4f54-a17e-dc796256864d/1873-4
00:09:11.421 --> 00:09:14.694
if this model class will write,
would you have absorbed these

bda32352-a5ee-4f54-a17e-dc796256864d/1873-5
00:09:14.694 --> 00:09:15.010
datas?

bda32352-a5ee-4f54-a17e-dc796256864d/1880-0
00:09:15.500 --> 00:09:16.570
You shouldn't think about that,
right?

bda32352-a5ee-4f54-a17e-dc796256864d/1886-0
00:09:16.580 --> 00:09:17.490
Because it's George, Box said.

bda32352-a5ee-4f54-a17e-dc796256864d/1898-0
00:09:17.500 --> 00:09:19.720
Or models are wrong, but some
are useful.

bda32352-a5ee-4f54-a17e-dc796256864d/1927-0
00:09:19.960 --> 00:09:23.530
No model is right, and Bayesian
analysis knows this, but it's

bda32352-a5ee-4f54-a17e-dc796256864d/1927-1
00:09:23.530 --> 00:09:27.041
basically it's a useful metric
that tells you about how good

bda32352-a5ee-4f54-a17e-dc796256864d/1927-2
00:09:27.041 --> 00:09:28.250
your model design is.

bda32352-a5ee-4f54-a17e-dc796256864d/1941-0
00:09:28.260 --> 00:09:31.167
Would you actually expect to see
data like this given that model

bda32352-a5ee-4f54-a17e-dc796256864d/1941-1
00:09:31.167 --> 00:09:31.480
design?

bda32352-a5ee-4f54-a17e-dc796256864d/1960-0
00:09:32.120 --> 00:09:34.753
Umm, unfortunately we don't have
to actually really get to look

bda32352-a5ee-4f54-a17e-dc796256864d/1960-1
00:09:34.753 --> 00:09:35.370
at that number.

bda32352-a5ee-4f54-a17e-dc796256864d/1990-0
00:09:35.700 --> 00:09:39.271
If you do some math, you'll find
out that it turns out to be the

bda32352-a5ee-4f54-a17e-dc796256864d/1990-1
00:09:39.271 --> 00:09:42.567
integral over all values of all
possible values of all your

bda32352-a5ee-4f54-a17e-dc796256864d/1990-2
00:09:42.567 --> 00:09:43.500
model parameters.

bda32352-a5ee-4f54-a17e-dc796256864d/2002-0
00:09:43.520 --> 00:09:46.990
It's like really hard to I'm
actually evaluate.

bda32352-a5ee-4f54-a17e-dc796256864d/2017-0
00:09:47.080 --> 00:09:50.938
So when reality we always write
this as a proportionality,

bda32352-a5ee-4f54-a17e-dc796256864d/2017-1
00:09:50.938 --> 00:09:51.330
right?

bda32352-a5ee-4f54-a17e-dc796256864d/2037-0
00:09:52.380 --> 00:09:55.353
The posterior is proportional to
the data likelihood times the

bda32352-a5ee-4f54-a17e-dc796256864d/2037-1
00:09:55.353 --> 00:09:56.390
file, and that's just.

bda32352-a5ee-4f54-a17e-dc796256864d/2042-0
00:09:56.400 --> 00:09:57.780
Forget about that denominator.

bda32352-a5ee-4f54-a17e-dc796256864d/2051-0
00:09:58.640 --> 00:10:00.070
Umm, so that's all and so.

bda32352-a5ee-4f54-a17e-dc796256864d/2056-0
00:10:00.080 --> 00:10:00.980
And how do we get this?

bda32352-a5ee-4f54-a17e-dc796256864d/2078-0
00:10:00.990 --> 00:10:04.450
Like, how do we actually compute
the posterior distribution and

bda32352-a5ee-4f54-a17e-dc796256864d/2078-1
00:10:04.450 --> 00:10:07.260
the way that we do this is
through sampling, right?

bda32352-a5ee-4f54-a17e-dc796256864d/2148-0
00:10:07.320 --> 00:10:10.384
Just draw random samples with
density proportional to the

bda32352-a5ee-4f54-a17e-dc796256864d/2148-1
00:10:10.384 --> 00:10:13.659
target posterior PDF so that we
have a bunch of samples whose

bda32352-a5ee-4f54-a17e-dc796256864d/2148-2
00:10:13.659 --> 00:10:16.776
mean is the meaning of posterior
PDF and the median is the

bda32352-a5ee-4f54-a17e-dc796256864d/2148-3
00:10:16.776 --> 00:10:20.103
median, and your posterior PDF
and the thing that holds 95% of

bda32352-a5ee-4f54-a17e-dc796256864d/2148-4
00:10:20.103 --> 00:10:22.480
those samples is your 95%
confidence bounds.

bda32352-a5ee-4f54-a17e-dc796256864d/2152-0
00:10:23.500 --> 00:10:23.820
Umm.

bda32352-a5ee-4f54-a17e-dc796256864d/2178-0
00:10:24.120 --> 00:10:27.479
So right, if you play around in
MATLAB or Python or whatever she

bda32352-a5ee-4f54-a17e-dc796256864d/2178-1
00:10:27.479 --> 00:10:30.630
like, no, you'll you'll see
random number generators, right?

bda32352-a5ee-4f54-a17e-dc796256864d/2206-0
00:10:30.640 --> 00:10:34.493
They they do specific tasks they
make normally distributed random

bda32352-a5ee-4f54-a17e-dc796256864d/2206-1
00:10:34.493 --> 00:10:37.703
numbers or uniform distributed
random numbers, but the

bda32352-a5ee-4f54-a17e-dc796256864d/2206-2
00:10:37.703 --> 00:10:39.570
posterior PDF could be anything.

bda32352-a5ee-4f54-a17e-dc796256864d/2221-0
00:10:39.940 --> 00:10:43.010
So how do you draw samples of an
arbitrary PDF?

bda32352-a5ee-4f54-a17e-dc796256864d/2240-0
00:10:43.340 --> 00:10:46.825
To do that, you basically need a
universal random number

bda32352-a5ee-4f54-a17e-dc796256864d/2240-1
00:10:46.825 --> 00:10:50.310
generator, and that is what the
Metropolis algorithm is.

bda32352-a5ee-4f54-a17e-dc796256864d/2252-0
00:10:50.320 --> 00:10:53.690
It's a random number generator
that walks for anything.

bda32352-a5ee-4f54-a17e-dc796256864d/2255-0
00:10:53.740 --> 00:10:54.210
It can.

bda32352-a5ee-4f54-a17e-dc796256864d/2262-0
00:10:54.260 --> 00:10:55.820
It's it's basically a random
walk.

bda32352-a5ee-4f54-a17e-dc796256864d/2319-0
00:10:55.830 --> 00:10:59.157
It's a Markov chain Monte Carlo
process that randomly decides

bda32352-a5ee-4f54-a17e-dc796256864d/2319-1
00:10:59.157 --> 00:11:02.537
whether or not to accept random
numbers that are generates and

bda32352-a5ee-4f54-a17e-dc796256864d/2319-2
00:11:02.537 --> 00:11:05.434
eventually we'll converge to
have samples distributed

bda32352-a5ee-4f54-a17e-dc796256864d/2319-3
00:11:05.434 --> 00:11:08.438
according to the posterior PDF
or whatever it is you're

bda32352-a5ee-4f54-a17e-dc796256864d/2319-4
00:11:08.438 --> 00:11:09.940
actually trying to simulate.

bda32352-a5ee-4f54-a17e-dc796256864d/2361-0
00:11:10.720 --> 00:11:13.208
It's called the Metropolis
algorithm, cause Foster pulled

bda32352-a5ee-4f54-a17e-dc796256864d/2361-1
00:11:13.208 --> 00:11:15.739
in this people 1953 general
chemical physics equations are

bda32352-a5ee-4f54-a17e-dc796256864d/2361-2
00:11:15.739 --> 00:11:18.312
state calculations by fast
computing machines but tropolis,

bda32352-a5ee-4f54-a17e-dc796256864d/2361-3
00:11:18.312 --> 00:11:20.070
Rosenbluth, Rosenbluth tallow,
and tell.

bda32352-a5ee-4f54-a17e-dc796256864d/2371-0
00:11:20.580 --> 00:11:22.330
We need to take a moment to talk
about this paper.

bda32352-a5ee-4f54-a17e-dc796256864d/2397-0
00:11:23.050 --> 00:11:26.861
Umm, the five authors on this
people are marshmallows and

bda32352-a5ee-4f54-a17e-dc796256864d/2397-1
00:11:26.861 --> 00:11:28.240
booth a grad student.

bda32352-a5ee-4f54-a17e-dc796256864d/2406-0
00:11:28.630 --> 00:11:30.150
His PhD advisor? Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/2402-0
00:11:28.850 --> 00:11:29.510
Hey Sarah.

bda32352-a5ee-4f54-a17e-dc796256864d/2407-0
00:11:30.900 --> 00:11:31.850
Sorry to interrupt you.

bda32352-a5ee-4f54-a17e-dc796256864d/2420-0
00:11:31.860 --> 00:11:35.770
I think we might be seeing some
slides that are getting stuck.

bda32352-a5ee-4f54-a17e-dc796256864d/2429-0
00:11:35.780 --> 00:11:37.370
What slide are you on?

bda32352-a5ee-4f54-a17e-dc796256864d/2431-0
00:11:38.290 --> 00:11:39.500
I'm on slide 10.

bda32352-a5ee-4f54-a17e-dc796256864d/2442-0
00:11:39.570 --> 00:11:41.540
You want me to so I.

bda32352-a5ee-4f54-a17e-dc796256864d/2447-0
00:11:40.830 --> 00:11:41.870
We're seeing like.

bda32352-a5ee-4f54-a17e-dc796256864d/2460-0
00:11:41.590 --> 00:11:45.750
Somebody, somebody seems to have
taken control away from me.

bda32352-a5ee-4f54-a17e-dc796256864d/2461-0
00:11:45.870 --> 00:11:46.670
I think it's.

bda32352-a5ee-4f54-a17e-dc796256864d/2466-0
00:11:46.730 --> 00:11:48.960
I think it's our Magar it.

bda32352-a5ee-4f54-a17e-dc796256864d/2474-0
00:11:49.010 --> 00:11:49.480
Ohh no.

bda32352-a5ee-4f54-a17e-dc796256864d/2479-0
00:11:49.530 --> 00:11:50.630
Now it's just Sarah Minson.

bda32352-a5ee-4f54-a17e-dc796256864d/2477-0
00:11:49.540 --> 00:11:49.960
OK.

bda32352-a5ee-4f54-a17e-dc796256864d/2485-0
00:11:51.780 --> 00:11:52.930
Yeah, yeah, sure.

bda32352-a5ee-4f54-a17e-dc796256864d/2486-0
00:11:53.520 --> 00:11:53.760
No.

bda32352-a5ee-4f54-a17e-dc796256864d/2493-0
00:11:55.690 --> 00:11:56.550
Alright, just now in charge.

bda32352-a5ee-4f54-a17e-dc796256864d/2515-0
00:11:58.430 --> 00:12:02.930
OK, so so now I now we see Slide
10 is everything.

bda32352-a5ee-4f54-a17e-dc796256864d/2504-0
00:11:58.600 --> 00:11:58.880
So.

bda32352-a5ee-4f54-a17e-dc796256864d/2514-0
00:12:01.140 --> 00:12:01.840
Yeah, yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/2518-0
00:12:01.940 --> 00:12:02.220
OK.

bda32352-a5ee-4f54-a17e-dc796256864d/2551-0
00:12:03.130 --> 00:12:07.910
Is everybody good and and do you
wanna flip forward and back just

bda32352-a5ee-4f54-a17e-dc796256864d/2549-0
00:12:07.060 --> 00:12:09.630
That not everyone.

bda32352-a5ee-4f54-a17e-dc796256864d/2551-1
00:12:07.910 --> 00:12:11.240
to make sure that you can do
that in a OK 76?

bda32352-a5ee-4f54-a17e-dc796256864d/2553-0
00:12:11.320 --> 00:12:11.860
Great.

bda32352-a5ee-4f54-a17e-dc796256864d/2561-0
00:12:11.870 --> 00:12:13.120
Sorry to interrupt, Siri.

bda32352-a5ee-4f54-a17e-dc796256864d/2565-0
00:12:13.530 --> 00:12:13.860
Great.

bda32352-a5ee-4f54-a17e-dc796256864d/2570-0
00:12:13.580 --> 00:12:14.910
No, thank you for letting me.

bda32352-a5ee-4f54-a17e-dc796256864d/2575-0
00:12:13.870 --> 00:12:14.310
Talk to you.

bda32352-a5ee-4f54-a17e-dc796256864d/2579-0
00:12:14.920 --> 00:12:16.150
I wasn't sure.

bda32352-a5ee-4f54-a17e-dc796256864d/2607-0
00:12:16.240 --> 00:12:18.646
It seemed a little bit weird
that it had a real that it the

bda32352-a5ee-4f54-a17e-dc796256864d/2607-1
00:12:18.646 --> 00:12:20.690
screen had suddenly changed and
I didn't know why.

bda32352-a5ee-4f54-a17e-dc796256864d/2613-0
00:12:21.760 --> 00:12:22.810
Just real fast.

bda32352-a5ee-4f54-a17e-dc796256864d/2617-0
00:12:22.240 --> 00:12:22.640
Alright.

bda32352-a5ee-4f54-a17e-dc796256864d/2649-0
00:12:22.860 --> 00:12:26.643
If you're not seeing the correct
slide, go to the bottom of the

bda32352-a5ee-4f54-a17e-dc796256864d/2649-1
00:12:26.643 --> 00:12:30.071
screen and click the right
button to navigate forward and

bda32352-a5ee-4f54-a17e-dc796256864d/2649-2
00:12:30.071 --> 00:12:33.439
teams will give you an option to
sync your view with the

bda32352-a5ee-4f54-a17e-dc796256864d/2649-3
00:12:33.439 --> 00:12:34.030
presenter.

bda32352-a5ee-4f54-a17e-dc796256864d/2665-0
00:12:34.770 --> 00:12:35.670
It's a new feature.

bda32352-a5ee-4f54-a17e-dc796256864d/2682-0
00:12:34.980 --> 00:12:37.305
Course if somebody else decides
to take over presenting, that's

bda32352-a5ee-4f54-a17e-dc796256864d/2682-1
00:12:37.305 --> 00:12:38.140
not gonna help us much.

bda32352-a5ee-4f54-a17e-dc796256864d/2683-0
00:12:38.430 --> 00:12:40.030
Yeah, I tried that and it did.

bda32352-a5ee-4f54-a17e-dc796256864d/2690-0
00:12:40.040 --> 00:12:41.600
That's where it said art Mcgarr.

bda32352-a5ee-4f54-a17e-dc796256864d/2698-0
00:12:41.610 --> 00:12:42.850
But now it doesn't so.

bda32352-a5ee-4f54-a17e-dc796256864d/2709-0
00:12:43.960 --> 00:12:44.120
It's.

bda32352-a5ee-4f54-a17e-dc796256864d/2711-0
00:12:44.110 --> 00:12:47.080
OK, nobody steal the slides.

bda32352-a5ee-4f54-a17e-dc796256864d/2712-0
00:12:46.840 --> 00:12:47.220
Stupid.

bda32352-a5ee-4f54-a17e-dc796256864d/2714-0
00:12:47.610 --> 00:12:48.020
I don't think.

bda32352-a5ee-4f54-a17e-dc796256864d/2724-0
00:12:48.300 --> 00:12:50.380
Yes, thank you, Sarah.

bda32352-a5ee-4f54-a17e-dc796256864d/2726-0
00:12:50.240 --> 00:12:51.940
Keep keep going, Sarah.

bda32352-a5ee-4f54-a17e-dc796256864d/2746-0
00:12:52.670 --> 00:12:57.833
OK, umm SO5 authors Metropolis
Rosenbluth, Rosenbluth, tell one

bda32352-a5ee-4f54-a17e-dc796256864d/2746-1
00:12:57.833 --> 00:12:58.720
Tello Rosa.

bda32352-a5ee-4f54-a17e-dc796256864d/2758-0
00:12:58.730 --> 00:13:01.679
Rosenbluth was a grad student
Edward Teller was his PhD

bda32352-a5ee-4f54-a17e-dc796256864d/2758-1
00:13:01.679 --> 00:13:02.100
advisor.

bda32352-a5ee-4f54-a17e-dc796256864d/2766-0
00:13:02.210 --> 00:13:03.500
Yes, that Edward teller.

bda32352-a5ee-4f54-a17e-dc796256864d/2783-0
00:13:03.510 --> 00:13:05.733
In fact, these will computations
there I believe were done as

bda32352-a5ee-4f54-a17e-dc796256864d/2783-1
00:13:05.733 --> 00:13:06.700
part of the H Bomb project.

bda32352-a5ee-4f54-a17e-dc796256864d/2816-0
00:13:07.170 --> 00:13:11.569
There are the two people who
actually implemented this this

bda32352-a5ee-4f54-a17e-dc796256864d/2816-1
00:13:11.569 --> 00:13:15.967
algorithm to run on the maniac
machine in Los Alamos, Rosen

bda32352-a5ee-4f54-a17e-dc796256864d/2816-2
00:13:15.967 --> 00:13:17.140
Blues and total.

bda32352-a5ee-4f54-a17e-dc796256864d/2828-0
00:13:17.500 --> 00:13:20.670
And then there is the guy who
owned the computer.

bda32352-a5ee-4f54-a17e-dc796256864d/2884-0
00:13:21.160 --> 00:13:24.885
Somehow that got him his name on
the people and enforced position

bda32352-a5ee-4f54-a17e-dc796256864d/2884-1
00:13:24.885 --> 00:13:28.383
and thus the algorithm is named
after him, even though he had

bda32352-a5ee-4f54-a17e-dc796256864d/2884-2
00:13:28.383 --> 00:13:31.318
nothing to do with it, and in
fact there was a 50th

bda32352-a5ee-4f54-a17e-dc796256864d/2884-3
00:13:31.318 --> 00:13:34.703
anniversary symposium at Los
Alamos in 2005 that Governates

bda32352-a5ee-4f54-a17e-dc796256864d/2884-4
00:13:34.703 --> 00:13:35.380
wrote about.

bda32352-a5ee-4f54-a17e-dc796256864d/2945-0
00:13:36.370 --> 00:13:39.513
There was like, it's very clear
that Metropolis was not involved

bda32352-a5ee-4f54-a17e-dc796256864d/2945-1
00:13:39.513 --> 00:13:42.463
it the algorithm, the Metropolis
algorithm, the thing that's

bda32352-a5ee-4f54-a17e-dc796256864d/2945-2
00:13:42.463 --> 00:13:45.267
called the Metropolis algorithm,
was developed by Arianna

bda32352-a5ee-4f54-a17e-dc796256864d/2945-3
00:13:45.267 --> 00:13:47.539
Rosenbluth and Marshall
Rosenbluth and Arianna

bda32352-a5ee-4f54-a17e-dc796256864d/2945-4
00:13:47.539 --> 00:13:50.440
Rosenbluth was the one who
implemented it to run on maniac.

bda32352-a5ee-4f54-a17e-dc796256864d/2962-0
00:13:50.450 --> 00:13:52.790
So it should really be called
the Rosenbluth and Rosenbluth

bda32352-a5ee-4f54-a17e-dc796256864d/2962-1
00:13:52.790 --> 00:13:53.180
algorithm.

bda32352-a5ee-4f54-a17e-dc796256864d/2981-0
00:13:54.590 --> 00:13:57.180
I also just want to take a
moment to to shout out the code.

bda32352-a5ee-4f54-a17e-dc796256864d/2987-0
00:13:57.190 --> 00:13:57.920
Also walked on this.

bda32352-a5ee-4f54-a17e-dc796256864d/2996-0
00:13:57.930 --> 00:14:01.340
I mean, these are the bad days
of coding, right?

bda32352-a5ee-4f54-a17e-dc796256864d/3036-0
00:14:01.430 --> 00:14:06.063
Like Grace Hopper only proposed
the concept of computer language

bda32352-a5ee-4f54-a17e-dc796256864d/3036-1
00:14:06.063 --> 00:14:10.624
compiler in 1950, right up until
then, like people will writing

bda32352-a5ee-4f54-a17e-dc796256864d/3036-2
00:14:10.624 --> 00:14:14.330
code for computer was like he
was a wiring diagram.

bda32352-a5ee-4f54-a17e-dc796256864d/3049-0
00:14:14.340 --> 00:14:16.580
Make this machine do something
right.

bda32352-a5ee-4f54-a17e-dc796256864d/3056-0
00:14:16.690 --> 00:14:20.195
In 1953, writing code for
something like Maniac was

bda32352-a5ee-4f54-a17e-dc796256864d/3056-1
00:14:20.195 --> 00:14:21.610
incredibly difficult.

bda32352-a5ee-4f54-a17e-dc796256864d/3061-0
00:14:21.620 --> 00:14:22.900
It was really hard.

bda32352-a5ee-4f54-a17e-dc796256864d/3069-0
00:14:22.910 --> 00:14:24.370
It was almost impossible to do.

bda32352-a5ee-4f54-a17e-dc796256864d/3115-0
00:14:24.850 --> 00:14:28.066
It was women's walk and these
are photos from the archive at

bda32352-a5ee-4f54-a17e-dc796256864d/3115-1
00:14:28.066 --> 00:14:31.229
Los Alamos and I guess it wasn't
really well respected work

bda32352-a5ee-4f54-a17e-dc796256864d/3115-2
00:14:31.229 --> 00:14:34.655
either, because only one of them
bothered to identify the person

bda32352-a5ee-4f54-a17e-dc796256864d/3115-3
00:14:34.655 --> 00:14:35.340
in the photo.

bda32352-a5ee-4f54-a17e-dc796256864d/3165-0
00:14:36.680 --> 00:14:40.615
Umm, so I just want to mention
that the really unbelievably

bda32352-a5ee-4f54-a17e-dc796256864d/3165-1
00:14:40.615 --> 00:14:44.352
difficult task of writing the
forced MCMC algorithm ever

bda32352-a5ee-4f54-a17e-dc796256864d/3165-2
00:14:44.352 --> 00:14:47.828
devised and making it run on
maniac fell to Marshall

bda32352-a5ee-4f54-a17e-dc796256864d/3165-3
00:14:47.828 --> 00:14:50.450
Rosenbluth and Edward Teller was
vibes.

bda32352-a5ee-4f54-a17e-dc796256864d/3169-0
00:14:50.460 --> 00:14:52.290
Arianna Rosenbluth and Augusta
Tello.

bda32352-a5ee-4f54-a17e-dc796256864d/3185-0
00:14:55.230 --> 00:14:59.384
OK, so Markov chain Monte Carlo
sampling Ed will walk

bda32352-a5ee-4f54-a17e-dc796256864d/3185-1
00:14:59.384 --> 00:15:00.230
eventually.

bda32352-a5ee-4f54-a17e-dc796256864d/3191-0
00:15:00.300 --> 00:15:01.270
It works for everything.

bda32352-a5ee-4f54-a17e-dc796256864d/3204-0
00:15:01.280 --> 00:15:03.800
Eventually you will get samples
and distributed according to

bda32352-a5ee-4f54-a17e-dc796256864d/3204-1
00:15:03.800 --> 00:15:04.460
your target PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/3214-0
00:15:05.200 --> 00:15:07.330
It may take a very, very, very
long time.

bda32352-a5ee-4f54-a17e-dc796256864d/3222-0
00:15:07.340 --> 00:15:08.710
We might all be dead forced.

bda32352-a5ee-4f54-a17e-dc796256864d/3259-0
00:15:08.840 --> 00:15:11.178
So ever since then, people
basically have been doing

bda32352-a5ee-4f54-a17e-dc796256864d/3259-1
00:15:11.178 --> 00:15:13.825
variations on the tropolis
algorithms trying to find clever

bda32352-a5ee-4f54-a17e-dc796256864d/3259-2
00:15:13.825 --> 00:15:16.428
ways to make it more efficient
to get an answer with fewer

bda32352-a5ee-4f54-a17e-dc796256864d/3259-3
00:15:16.428 --> 00:15:16.780
samples.

bda32352-a5ee-4f54-a17e-dc796256864d/3308-0
00:15:18.600 --> 00:15:21.670
It was a really great idea that
came was come up with my Beck

bda32352-a5ee-4f54-a17e-dc796256864d/3308-1
00:15:21.670 --> 00:15:24.689
and Allen 2002 and they said,
well, if you could construct a

bda32352-a5ee-4f54-a17e-dc796256864d/3308-2
00:15:24.689 --> 00:15:27.759
series of intermediate PDFs,
they're lead from a known PDF to

bda32352-a5ee-4f54-a17e-dc796256864d/3308-3
00:15:27.759 --> 00:15:29.590
the thing you're trying to
simulate.

bda32352-a5ee-4f54-a17e-dc796256864d/3330-0
00:15:29.860 --> 00:15:33.198
Then it will be relatively easy
to make your random walk your

bda32352-a5ee-4f54-a17e-dc796256864d/3330-1
00:15:33.198 --> 00:15:36.427
MCMC converge to the thing you
actually trying to simulate,

bda32352-a5ee-4f54-a17e-dc796256864d/3330-2
00:15:36.427 --> 00:15:36.750
right?

bda32352-a5ee-4f54-a17e-dc796256864d/3344-0
00:15:36.760 --> 00:15:38.810
It's like coding a laser pointer
in front of a cat.

bda32352-a5ee-4f54-a17e-dc796256864d/3368-0
00:15:38.900 --> 00:15:41.433
The cat is still doing a random
rock, but it's a random walk

bda32352-a5ee-4f54-a17e-dc796256864d/3368-1
00:15:41.433 --> 00:15:43.800
that goes directly to the place
you're trying to get to.

bda32352-a5ee-4f54-a17e-dc796256864d/3376-0
00:15:45.020 --> 00:15:46.750
So what all these intermediate
PDF's?

bda32352-a5ee-4f54-a17e-dc796256864d/3424-0
00:15:46.760 --> 00:15:49.685
As well, in 2007, Ching and Chen
came up with a really great

bda32352-a5ee-4f54-a17e-dc796256864d/3424-1
00:15:49.685 --> 00:15:52.657
idea, which is that well, if
you're doing a Bayesian problem,

bda32352-a5ee-4f54-a17e-dc796256864d/3424-2
00:15:52.657 --> 00:15:55.629
if you're trying to get to a
posterior PDF, what you could do

bda32352-a5ee-4f54-a17e-dc796256864d/3424-3
00:15:55.629 --> 00:15:57.450
is you can start with your prior
PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/3427-0
00:15:57.540 --> 00:15:58.490
You pick that.

bda32352-a5ee-4f54-a17e-dc796256864d/3452-0
00:15:58.550 --> 00:16:00.975
Pick that to be something you
can directly simulate, like a

bda32352-a5ee-4f54-a17e-dc796256864d/3452-1
00:16:00.975 --> 00:16:03.400
uniform distribution or a normal
distribution or something.

bda32352-a5ee-4f54-a17e-dc796256864d/3550-0
00:16:03.620 --> 00:16:06.876
And then imagine putting an
exponential on your likelihood,

bda32352-a5ee-4f54-a17e-dc796256864d/3550-1
00:16:06.876 --> 00:16:09.861
and if you start that
exponential at zero, then you'll

bda32352-a5ee-4f54-a17e-dc796256864d/3550-2
00:16:09.861 --> 00:16:13.280
get your prior PDF and you just
draw samples of your prior PDF

bda32352-a5ee-4f54-a17e-dc796256864d/3550-3
00:16:13.280 --> 00:16:16.265
from a random number generator,
and then you make your

bda32352-a5ee-4f54-a17e-dc796256864d/3550-4
00:16:16.265 --> 00:16:19.304
exponential be something
slightly greater than one, and

bda32352-a5ee-4f54-a17e-dc796256864d/3550-5
00:16:19.304 --> 00:16:22.288
you do some random walking to
make your examples be at

bda32352-a5ee-4f54-a17e-dc796256864d/3550-6
00:16:22.288 --> 00:16:25.490
equilibrium with just a little
bit of input from your data

bda32352-a5ee-4f54-a17e-dc796256864d/3550-7
00:16:25.490 --> 00:16:28.963
likelihood, and you increase and
you increase and increase, and

bda32352-a5ee-4f54-a17e-dc796256864d/3550-8
00:16:28.963 --> 00:16:32.273
eventually you get up to having
an exponential equal to what

bda32352-a5ee-4f54-a17e-dc796256864d/3550-9
00:16:32.273 --> 00:16:32.490
one.

bda32352-a5ee-4f54-a17e-dc796256864d/3582-0
00:16:32.500 --> 00:16:34.975
So it's your actually the
product of your likelihood and

bda32352-a5ee-4f54-a17e-dc796256864d/3582-1
00:16:34.975 --> 00:16:37.709
your prior and then your samples
are actually distributed into

bda32352-a5ee-4f54-a17e-dc796256864d/3582-2
00:16:37.709 --> 00:16:38.360
your posterior.

bda32352-a5ee-4f54-a17e-dc796256864d/3610-0
00:16:39.250 --> 00:16:42.015
And because you all guiding your
samples on the prior to the

bda32352-a5ee-4f54-a17e-dc796256864d/3610-1
00:16:42.015 --> 00:16:44.870
posterior, this is a lot faster
than the metropolis should be.

bda32352-a5ee-4f54-a17e-dc796256864d/3632-0
00:16:44.880 --> 00:16:48.387
Rosenbluth algorithm that has to
wander through the entire space

bda32352-a5ee-4f54-a17e-dc796256864d/3632-1
00:16:48.387 --> 00:16:51.571
of real numbers to figure out
what the posterior PDF looks

bda32352-a5ee-4f54-a17e-dc796256864d/3632-2
00:16:51.571 --> 00:16:51.840
like.

bda32352-a5ee-4f54-a17e-dc796256864d/3642-0
00:16:54.960 --> 00:16:56.570
So in grad school.

bda32352-a5ee-4f54-a17e-dc796256864d/3646-0
00:16:56.920 --> 00:16:57.590
But I did.

bda32352-a5ee-4f54-a17e-dc796256864d/3675-0
00:16:57.600 --> 00:17:00.810
Was we developed catnip, which
was a which is a parallel and

bda32352-a5ee-4f54-a17e-dc796256864d/3675-1
00:17:00.810 --> 00:17:03.915
efficient version of this
transitioning Markov chain Monte

bda32352-a5ee-4f54-a17e-dc796256864d/3675-2
00:17:03.915 --> 00:17:04.230
Carlo.

bda32352-a5ee-4f54-a17e-dc796256864d/3708-0
00:17:04.240 --> 00:17:07.740
The Ching in Chen developed and
then we use that to make a fully

bda32352-a5ee-4f54-a17e-dc796256864d/3708-1
00:17:07.740 --> 00:17:11.025
Bayesian unsmoothed rupture
model of the 2011 magnitude 9 to

bda32352-a5ee-4f54-a17e-dc796256864d/3708-2
00:17:11.025 --> 00:17:11.940
hokey earthquake.

bda32352-a5ee-4f54-a17e-dc796256864d/3741-0
00:17:13.070 --> 00:17:16.463
That motto has 866 free
parameters, 2 components of slip

bda32352-a5ee-4f54-a17e-dc796256864d/3741-1
00:17:16.463 --> 00:17:20.152
rise time and rupture velocity
on each of 219 four patches it

bda32352-a5ee-4f54-a17e-dc796256864d/3741-2
00:17:20.152 --> 00:17:20.390
has.

bda32352-a5ee-4f54-a17e-dc796256864d/3778-0
00:17:20.440 --> 00:17:23.384
It solves for the hotel on the
fault plane and it required

bda32352-a5ee-4f54-a17e-dc796256864d/3778-1
00:17:23.384 --> 00:17:26.477
about 60 billion MCMC samples
that were drawn over the course

bda32352-a5ee-4f54-a17e-dc796256864d/3778-2
00:17:26.477 --> 00:17:29.270
of a couple of days on the NASA
Pleiades supercomputer.

bda32352-a5ee-4f54-a17e-dc796256864d/3791-0
00:17:30.850 --> 00:17:34.130
So all of this walk has made
this problem doable.

bda32352-a5ee-4f54-a17e-dc796256864d/3799-0
00:17:34.970 --> 00:17:35.920
Is not made the problem.

bda32352-a5ee-4f54-a17e-dc796256864d/3811-0
00:17:35.930 --> 00:17:37.980
Fun it's requires a couple of
days in a super computer.

bda32352-a5ee-4f54-a17e-dc796256864d/3866-0
00:17:38.740 --> 00:17:41.773
Umm, so in the back of my mind I
always wanted to like be able to

bda32352-a5ee-4f54-a17e-dc796256864d/3866-1
00:17:41.773 --> 00:17:44.667
revisit this problem and say can
we make this problem not just

bda32352-a5ee-4f54-a17e-dc796256864d/3866-2
00:17:44.667 --> 00:17:47.286
doable on a super computer but
something that's fun on a

bda32352-a5ee-4f54-a17e-dc796256864d/3866-3
00:17:47.286 --> 00:17:50.089
desktop computer so that it's
actually accessible and doable

bda32352-a5ee-4f54-a17e-dc796256864d/3866-4
00:17:50.089 --> 00:17:50.640
by everyone.

bda32352-a5ee-4f54-a17e-dc796256864d/3906-0
00:17:51.410 --> 00:17:54.601
And then meanwhile, I want 2014
the magnitude 6 S and upper

bda32352-a5ee-4f54-a17e-dc796256864d/3906-1
00:17:54.601 --> 00:17:58.057
earthquake happens and my friend
Ben goes out and he collects 10

bda32352-a5ee-4f54-a17e-dc796256864d/3906-2
00:17:58.057 --> 00:18:00.290
million light off point returns
at image.

bda32352-a5ee-4f54-a17e-dc796256864d/3912-0
00:18:00.300 --> 00:18:00.970
The upshot itself?

bda32352-a5ee-4f54-a17e-dc796256864d/3985-0
00:18:00.980 --> 00:18:04.191
Meter scale and my friend Josie
goes out and she starts taking

bda32352-a5ee-4f54-a17e-dc796256864d/3985-1
00:18:04.191 --> 00:18:07.301
samples and doing experiments to
look at the theology of the

bda32352-a5ee-4f54-a17e-dc796256864d/3985-2
00:18:07.301 --> 00:18:10.563
shallow subsurface, and she sees
that there's all these changes

bda32352-a5ee-4f54-a17e-dc796256864d/3985-3
00:18:10.563 --> 00:18:13.315
and we already they're
controlling the rushall on the

bda32352-a5ee-4f54-a17e-dc796256864d/3985-4
00:18:13.315 --> 00:18:16.322
submittal scale and this all has
enormous implications for

bda32352-a5ee-4f54-a17e-dc796256864d/3985-5
00:18:16.322 --> 00:18:17.800
impacts on don't environment.

bda32352-a5ee-4f54-a17e-dc796256864d/4025-0
00:18:17.940 --> 00:18:20.678
So we need to be able to
understand the physics of this

bda32352-a5ee-4f54-a17e-dc796256864d/4025-1
00:18:20.678 --> 00:18:23.417
earthquake we need on the
submittal scale, so we need a

bda32352-a5ee-4f54-a17e-dc796256864d/4025-2
00:18:23.417 --> 00:18:26.252
webshow model for these data
that are free from arbitrary

bda32352-a5ee-4f54-a17e-dc796256864d/4025-3
00:18:26.252 --> 00:18:27.670
regularization and smoothing.

bda32352-a5ee-4f54-a17e-dc796256864d/4063-0
00:18:27.740 --> 00:18:31.720
And can image thought mechanics
on a sub meter scale, so we need

bda32352-a5ee-4f54-a17e-dc796256864d/4063-1
00:18:31.720 --> 00:18:35.026
the fully Bayesian webshow
model, but we need it on a

bda32352-a5ee-4f54-a17e-dc796256864d/4063-2
00:18:35.026 --> 00:18:36.250
submittal scale and.

bda32352-a5ee-4f54-a17e-dc796256864d/4067-0
00:18:36.360 --> 00:18:36.820
OK.

bda32352-a5ee-4f54-a17e-dc796256864d/4105-0
00:18:36.830 --> 00:18:40.669
Well, Tohoku was 29 kilometer
patch sizes fewer than 1000 feet

bda32352-a5ee-4f54-a17e-dc796256864d/4105-1
00:18:40.669 --> 00:18:44.507
parameters, but that be quiet 60
billion samples and days on a

bda32352-a5ee-4f54-a17e-dc796256864d/4105-2
00:18:44.507 --> 00:18:47.370
super computer to do the South
and all create.

bda32352-a5ee-4f54-a17e-dc796256864d/4117-0
00:18:47.380 --> 00:18:50.380
We're talking about a 10,000
times increase in spatial

bda32352-a5ee-4f54-a17e-dc796256864d/4117-1
00:18:50.380 --> 00:18:50.980
resolution.

bda32352-a5ee-4f54-a17e-dc796256864d/4160-0
00:18:51.540 --> 00:18:54.873
Umm, which means proportionately
more free parameters every time

bda32352-a5ee-4f54-a17e-dc796256864d/4160-1
00:18:54.873 --> 00:18:58.051
you increase the number of free
parameters you need orders of

bda32352-a5ee-4f54-a17e-dc796256864d/4160-2
00:18:58.051 --> 00:19:01.281
magnitude more MCMC samples, so
you're talking about orders of

bda32352-a5ee-4f54-a17e-dc796256864d/4160-3
00:19:01.281 --> 00:19:03.690
magnitude of orders of magnitude
more samples.

bda32352-a5ee-4f54-a17e-dc796256864d/4171-0
00:19:05.120 --> 00:19:06.930
I don't know how long this is
going to take.

bda32352-a5ee-4f54-a17e-dc796256864d/4184-0
00:19:06.940 --> 00:19:09.590
How long does it take for the
universe to die like this?

bda32352-a5ee-4f54-a17e-dc796256864d/4201-0
00:19:09.690 --> 00:19:13.363
This is just not even possible,
and that's just talking about

bda32352-a5ee-4f54-a17e-dc796256864d/4201-1
00:19:13.363 --> 00:19:14.370
the model, right?

bda32352-a5ee-4f54-a17e-dc796256864d/4244-0
00:19:14.440 --> 00:19:17.280
The fact that they are 10
million lidar point, which ones

bda32352-a5ee-4f54-a17e-dc796256864d/4244-1
00:19:17.280 --> 00:19:20.314
in itself is gonna kill this
because like every time you draw

bda32352-a5ee-4f54-a17e-dc796256864d/4244-2
00:19:20.314 --> 00:19:23.056
an MCMC sample, you have to
calculate the misfit to the

bda32352-a5ee-4f54-a17e-dc796256864d/4244-3
00:19:23.056 --> 00:19:23.300
data.

bda32352-a5ee-4f54-a17e-dc796256864d/4290-0
00:19:24.150 --> 00:19:27.631
And if your data is huge, even
if it's as simple as just

bda32352-a5ee-4f54-a17e-dc796256864d/4290-1
00:19:27.631 --> 00:19:31.294
calculating, you know d -, G
times your model parameters CD

bda32352-a5ee-4f54-a17e-dc796256864d/4290-2
00:19:31.294 --> 00:19:34.957
invoice d -, 2 times the model
parameters like the simplest

bda32352-a5ee-4f54-a17e-dc796256864d/4290-3
00:19:34.957 --> 00:19:36.300
possible linear model.

bda32352-a5ee-4f54-a17e-dc796256864d/4328-0
00:19:37.540 --> 00:19:41.527
If if you have a huge huge
number of data that is going to

bda32352-a5ee-4f54-a17e-dc796256864d/4328-1
00:19:41.527 --> 00:19:45.310
take a long time to compute
times, billions, trillions,

bda32352-a5ee-4f54-a17e-dc796256864d/4328-2
00:19:45.310 --> 00:19:49.364
quadrillions of samples like
just, no, none of this is even

bda32352-a5ee-4f54-a17e-dc796256864d/4328-3
00:19:49.364 --> 00:19:50.580
remotely possible.

bda32352-a5ee-4f54-a17e-dc796256864d/4349-0
00:19:50.690 --> 00:19:54.139
Like it's not in the realm of
possibility, but let's put it on

bda32352-a5ee-4f54-a17e-dc796256864d/4349-1
00:19:54.139 --> 00:19:56.110
the To Do List and everything
else.

bda32352-a5ee-4f54-a17e-dc796256864d/4352-0
00:19:56.200 --> 00:19:56.660
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/4362-0
00:19:56.670 --> 00:19:57.970
Somehow, we're gonna have to do
it.

bda32352-a5ee-4f54-a17e-dc796256864d/4400-0
00:19:57.980 --> 00:20:01.188
It's amedo scale and somehow
also we're gonna need to be able

bda32352-a5ee-4f54-a17e-dc796256864d/4400-1
00:20:01.188 --> 00:20:04.240
to utilize big data and I
continue to adorn the To Do List

bda32352-a5ee-4f54-a17e-dc796256864d/4400-2
00:20:04.240 --> 00:20:05.740
and we get up to around 2019.

bda32352-a5ee-4f54-a17e-dc796256864d/4461-0
00:20:05.750 --> 00:20:08.849
And my friend Jess is starting
to make Bayesian nuptial models

bda32352-a5ee-4f54-a17e-dc796256864d/4461-1
00:20:08.849 --> 00:20:11.997
for the Ridgecrest earthquakes,
and I am helping and by helping

bda32352-a5ee-4f54-a17e-dc796256864d/4461-2
00:20:11.997 --> 00:20:15.046
I mean standing next to her on
applauding, cuz this is really

bda32352-a5ee-4f54-a17e-dc796256864d/4461-3
00:20:15.046 --> 00:20:18.095
hard and I don't wanna do it and
we're talking about just how

bda32352-a5ee-4f54-a17e-dc796256864d/4461-4
00:20:18.095 --> 00:20:20.210
slow and painful these models
are to make.

bda32352-a5ee-4f54-a17e-dc796256864d/4472-0
00:20:20.270 --> 00:20:22.960
We really, we really need to do
something.

bda32352-a5ee-4f54-a17e-dc796256864d/4532-0
00:20:22.970 --> 00:20:26.361
We're talking about why this is
so painful and the reason that

bda32352-a5ee-4f54-a17e-dc796256864d/4532-1
00:20:26.361 --> 00:20:29.482
it's so painful is that, well,
OK, while transitioning is

bda32352-a5ee-4f54-a17e-dc796256864d/4532-2
00:20:29.482 --> 00:20:32.604
really neat and it makes it
possible to do these problems

bda32352-a5ee-4f54-a17e-dc796256864d/4532-3
00:20:32.604 --> 00:20:35.940
because we start at the prior
and we use the laser pointer to

bda32352-a5ee-4f54-a17e-dc796256864d/4532-4
00:20:35.940 --> 00:20:38.200
drag all of our samples to the
posterior.

bda32352-a5ee-4f54-a17e-dc796256864d/4578-0
00:20:39.760 --> 00:20:44.188
But if our prior is the space of
all things that are physically

bda32352-a5ee-4f54-a17e-dc796256864d/4578-1
00:20:44.188 --> 00:20:47.854
plausible, that's huge right
magnitude 3 earthquakes

bda32352-a5ee-4f54-a17e-dc796256864d/4578-2
00:20:47.854 --> 00:20:51.659
magnitude 8 earthquakes,
earthquakes with uniform step

bda32352-a5ee-4f54-a17e-dc796256864d/4578-3
00:20:51.659 --> 00:20:54.080
earthquakes with many
disparities.

bda32352-a5ee-4f54-a17e-dc796256864d/4591-0
00:20:54.230 --> 00:20:57.560
Earthquakes who slip is shaped
like a :).

bda32352-a5ee-4f54-a17e-dc796256864d/4609-0
00:20:57.850 --> 00:21:00.409
Like all of these, things are
physically plausible, only a few

bda32352-a5ee-4f54-a17e-dc796256864d/4609-1
00:21:00.409 --> 00:21:01.830
of these things will fit the
data.

bda32352-a5ee-4f54-a17e-dc796256864d/4652-0
00:21:03.320 --> 00:21:05.889
I mean, you could imagine that
it would be really much more

bda32352-a5ee-4f54-a17e-dc796256864d/4652-1
00:21:05.889 --> 00:21:08.629
efficient if you could reverse
the transitioning like you could

bda32352-a5ee-4f54-a17e-dc796256864d/4652-2
00:21:08.629 --> 00:21:11.284
start with models that fit the
data and then transition until

bda32352-a5ee-4f54-a17e-dc796256864d/4652-3
00:21:11.284 --> 00:21:13.210
they also agree with your prior
constraints.

bda32352-a5ee-4f54-a17e-dc796256864d/4658-0
00:21:14.200 --> 00:21:15.210
But that's not possible.

bda32352-a5ee-4f54-a17e-dc796256864d/4681-0
00:21:15.220 --> 00:21:17.825
If you could just start with a
bunch of things that fit the

bda32352-a5ee-4f54-a17e-dc796256864d/4681-1
00:21:17.825 --> 00:21:20.430
data, you wouldn't have invoiced
the OR you'd have invoice.

bda32352-a5ee-4f54-a17e-dc796256864d/4685-0
00:21:20.440 --> 00:21:20.830
Did I?

bda32352-a5ee-4f54-a17e-dc796256864d/4715-0
00:21:21.820 --> 00:21:26.128
Umm so I I went to talk to my
friend Matt and I said hey math,

bda32352-a5ee-4f54-a17e-dc796256864d/4715-1
00:21:26.128 --> 00:21:29.752
I I need to start this
transitioning from a PDF that

bda32352-a5ee-4f54-a17e-dc796256864d/4715-2
00:21:29.752 --> 00:21:30.640
fits my data.

bda32352-a5ee-4f54-a17e-dc796256864d/4723-0
00:21:30.850 --> 00:21:31.590
How do I do that?

bda32352-a5ee-4f54-a17e-dc796256864d/4737-0
00:21:32.680 --> 00:21:35.689
And my friend Matt said, well,
why you even simulating this

bda32352-a5ee-4f54-a17e-dc796256864d/4737-1
00:21:35.689 --> 00:21:36.390
posterior PDF?

bda32352-a5ee-4f54-a17e-dc796256864d/4777-0
00:21:36.400 --> 00:21:39.655
I mean, you have one of these
special problems that has an

bda32352-a5ee-4f54-a17e-dc796256864d/4777-1
00:21:39.655 --> 00:21:43.074
analytical solution and what
math means by this is, you know,

bda32352-a5ee-4f54-a17e-dc796256864d/4777-2
00:21:43.074 --> 00:21:46.273
if you'll just solving, you
know, a a lineal that's tasty

bda32352-a5ee-4f54-a17e-dc796256864d/4777-3
00:21:46.273 --> 00:21:47.100
problem, right.

bda32352-a5ee-4f54-a17e-dc796256864d/4785-0
00:21:47.110 --> 00:21:48.260
It's just a linear model.

bda32352-a5ee-4f54-a17e-dc796256864d/4794-0
00:21:48.630 --> 00:21:51.430
You'll you'll likelihood is just
an exponential.

bda32352-a5ee-4f54-a17e-dc796256864d/4809-0
00:21:51.440 --> 00:21:54.300
It's just a Gaussian around d -,
G times Theta.

bda32352-a5ee-4f54-a17e-dc796256864d/4892-0
00:21:55.420 --> 00:21:59.022
If you want to choose for your
prior a normal distribution,

bda32352-a5ee-4f54-a17e-dc796256864d/4892-1
00:21:59.022 --> 00:22:02.923
then you'll posterior would be a
Gaussian times a Gaussian which

bda32352-a5ee-4f54-a17e-dc796256864d/4892-2
00:22:02.923 --> 00:22:06.705
is equal to a Gaussian, and you
could just write down what the

bda32352-a5ee-4f54-a17e-dc796256864d/4892-3
00:22:06.705 --> 00:22:10.366
mean and covariance matrix of
your Gaussian posterior PDF is

bda32352-a5ee-4f54-a17e-dc796256864d/4892-4
00:22:10.366 --> 00:22:14.148
in fact fun fact, in the limit
that your prior covariance goes

bda32352-a5ee-4f54-a17e-dc796256864d/4892-5
00:22:14.148 --> 00:22:17.269
to Infinity, that is, that your
prior is completely

bda32352-a5ee-4f54-a17e-dc796256864d/4892-6
00:22:17.269 --> 00:22:19.970
uninformative and thus CM
invoice goes to 0.

bda32352-a5ee-4f54-a17e-dc796256864d/4900-0
00:22:20.580 --> 00:22:23.210
The Bayesian posterior is the
least squares solution.

bda32352-a5ee-4f54-a17e-dc796256864d/4983-0
00:22:23.220 --> 00:22:26.948
You probably low on least
squares as the least square or

bda32352-a5ee-4f54-a17e-dc796256864d/4983-1
00:22:26.948 --> 00:22:31.263
perpendicular distance, but it's
actually more fun to think of it

bda32352-a5ee-4f54-a17e-dc796256864d/4983-2
00:22:31.263 --> 00:22:34.925
as the maximum likelihood
estimate of a Bayesian linear

bda32352-a5ee-4f54-a17e-dc796256864d/4983-3
00:22:34.925 --> 00:22:39.110
regression, so this process will
buy there is a magic choice of

bda32352-a5ee-4f54-a17e-dc796256864d/4983-4
00:22:39.110 --> 00:22:43.425
prior that leads to a analytical
solution for your posterior, but

bda32352-a5ee-4f54-a17e-dc796256864d/4983-5
00:22:43.425 --> 00:22:47.479
also turns out to be the same
form as the prior itself, right

bda32352-a5ee-4f54-a17e-dc796256864d/4983-6
00:22:47.479 --> 00:22:51.010
up file with a Gaussian or
posterior with a Gaussian.

bda32352-a5ee-4f54-a17e-dc796256864d/4995-0
00:22:51.300 --> 00:22:53.090
This is known as the conjugate
trial.

bda32352-a5ee-4f54-a17e-dc796256864d/5002-0
00:22:53.240 --> 00:22:54.550
It's a terrible name.

bda32352-a5ee-4f54-a17e-dc796256864d/5012-0
00:22:54.680 --> 00:22:57.150
Most things in Bayesian analysis
have terrible names.

bda32352-a5ee-4f54-a17e-dc796256864d/5019-0
00:22:57.320 --> 00:22:58.910
It's just what it's called.

bda32352-a5ee-4f54-a17e-dc796256864d/5021-0
00:22:58.920 --> 00:22:59.230
I'm sorry.

bda32352-a5ee-4f54-a17e-dc796256864d/5044-0
00:23:01.540 --> 00:23:04.426
So math was like, you know, why
are you even bothering to

bda32352-a5ee-4f54-a17e-dc796256864d/5044-1
00:23:04.426 --> 00:23:05.670
simulate this poster PDF?

bda32352-a5ee-4f54-a17e-dc796256864d/5062-0
00:23:05.680 --> 00:23:09.372
Like does an analytical solution
and I said, but math I can't use

bda32352-a5ee-4f54-a17e-dc796256864d/5062-1
00:23:09.372 --> 00:23:10.490
that solution right?

bda32352-a5ee-4f54-a17e-dc796256864d/5066-0
00:23:10.500 --> 00:23:11.600
The prior is wrong.

bda32352-a5ee-4f54-a17e-dc796256864d/5080-0
00:23:11.610 --> 00:23:16.450
We don't think that earthquakes
look like Gaussians, right?

bda32352-a5ee-4f54-a17e-dc796256864d/5092-0
00:23:16.560 --> 00:23:18.620
There's we do think they look
like other things.

bda32352-a5ee-4f54-a17e-dc796256864d/5126-0
00:23:18.630 --> 00:23:21.636
If you think that they don't
slip backwards, but we don't

bda32352-a5ee-4f54-a17e-dc796256864d/5126-1
00:23:21.636 --> 00:23:24.694
think they, they look like
Gaussians and Masset fine, then

bda32352-a5ee-4f54-a17e-dc796256864d/5126-2
00:23:24.694 --> 00:23:27.440
use the conjugate posteo a PDF
as your starting PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/5156-0
00:23:27.450 --> 00:23:31.226
Right, because your posterior is
your likelihood times your

bda32352-a5ee-4f54-a17e-dc796256864d/5156-1
00:23:31.226 --> 00:23:34.938
prior, and you could, you know,
multiply that by something

bda32352-a5ee-4f54-a17e-dc796256864d/5156-2
00:23:34.938 --> 00:23:36.070
that's one, right?

bda32352-a5ee-4f54-a17e-dc796256864d/5190-0
00:23:36.080 --> 00:23:40.152
The ratio of the conjugate prior
to the conjugate file and the

bda32352-a5ee-4f54-a17e-dc796256864d/5190-1
00:23:40.152 --> 00:23:43.900
data likelihood times the
conjugate file is the conjugate

bda32352-a5ee-4f54-a17e-dc796256864d/5190-2
00:23:43.900 --> 00:23:47.260
pastorial, leaving leftover the
ratio of the prior.

bda32352-a5ee-4f54-a17e-dc796256864d/5220-0
00:23:47.270 --> 00:23:50.263
You did want to the prior that
you had to use to get to the

bda32352-a5ee-4f54-a17e-dc796256864d/5220-1
00:23:50.263 --> 00:23:53.005
conjugate posterior, and then
you could just slap some

bda32352-a5ee-4f54-a17e-dc796256864d/5220-2
00:23:53.005 --> 00:23:54.950
transitioning on that and you're
done.

bda32352-a5ee-4f54-a17e-dc796256864d/5281-0
00:23:57.020 --> 00:24:00.662
So, well before we started with
samples distributed according to

bda32352-a5ee-4f54-a17e-dc796256864d/5281-1
00:24:00.662 --> 00:24:04.359
our final and then use the laser
pointer to drag them to also fit

bda32352-a5ee-4f54-a17e-dc796256864d/5281-2
00:24:04.359 --> 00:24:07.664
our data likelihood, we're going
to start with samples and

bda32352-a5ee-4f54-a17e-dc796256864d/5281-3
00:24:07.664 --> 00:24:10.801
distributed according to some
analytical solution, some

bda32352-a5ee-4f54-a17e-dc796256864d/5281-4
00:24:10.801 --> 00:24:13.490
conjugate pastoral, and then
fade in the prior.

bda32352-a5ee-4f54-a17e-dc796256864d/5292-0
00:24:13.500 --> 00:24:16.730
We did one while we fade out the
prior.

bda32352-a5ee-4f54-a17e-dc796256864d/5316-0
00:24:16.740 --> 00:24:20.688
We didn't want to use the laser
point or to drag our samples

bda32352-a5ee-4f54-a17e-dc796256864d/5316-1
00:24:20.688 --> 00:24:23.730
from the conjugate posterior to
the posterior.

bda32352-a5ee-4f54-a17e-dc796256864d/5347-0
00:24:23.740 --> 00:24:26.395
We actually do want and
hopefully that requires a lot

bda32352-a5ee-4f54-a17e-dc796256864d/5347-1
00:24:26.395 --> 00:24:29.442
less MCMC, because since these
were all posteriors, they were

bda32352-a5ee-4f54-a17e-dc796256864d/5347-2
00:24:29.442 --> 00:24:31.310
all things that already fit our
data.

bda32352-a5ee-4f54-a17e-dc796256864d/5363-0
00:24:33.410 --> 00:24:37.400
So fade out the conjugate trial,
fade in the desired trial.

bda32352-a5ee-4f54-a17e-dc796256864d/5393-0
00:24:37.570 --> 00:24:40.743
It's like in lighting design or
sound design where you fade one

bda32352-a5ee-4f54-a17e-dc796256864d/5393-1
00:24:40.743 --> 00:24:43.370
so us out and fade another one
in it's cross fading.

bda32352-a5ee-4f54-a17e-dc796256864d/5406-0
00:24:46.900 --> 00:24:49.330
So let's let's show whether this
is efficient.

bda32352-a5ee-4f54-a17e-dc796256864d/5417-0
00:24:49.340 --> 00:24:52.030
So we're just going to do a
synthetic model.

bda32352-a5ee-4f54-a17e-dc796256864d/5431-0
00:24:52.140 --> 00:24:55.590
We're going to solve for fault
that has 72 patches on it.

bda32352-a5ee-4f54-a17e-dc796256864d/5500-0
00:24:55.600 --> 00:24:59.852
So 144 free parameters and we're
going to simulate the posterior

bda32352-a5ee-4f54-a17e-dc796256864d/5500-1
00:24:59.852 --> 00:25:03.972
PDF using three different sample
looks original tropolis which

bda32352-a5ee-4f54-a17e-dc796256864d/5500-2
00:25:03.972 --> 00:25:07.831
should be rosenbluth catnip
using transitioning and catnip

bda32352-a5ee-4f54-a17e-dc796256864d/5500-3
00:25:07.831 --> 00:25:11.690
using crossfading, and we're
going to see how well we will

bda32352-a5ee-4f54-a17e-dc796256864d/5500-4
00:25:11.690 --> 00:25:15.287
cover all the input model and
measured by the variance

bda32352-a5ee-4f54-a17e-dc796256864d/5500-5
00:25:15.287 --> 00:25:19.080
reduction as a function of the
number of samples we draw.

bda32352-a5ee-4f54-a17e-dc796256864d/5511-0
00:25:19.090 --> 00:25:20.650
And the question is what sample
or win?

bda32352-a5ee-4f54-a17e-dc796256864d/5518-0
00:25:20.880 --> 00:25:22.590
What sample will gets the best?

bda32352-a5ee-4f54-a17e-dc796256864d/5561-0
00:25:23.020 --> 00:25:26.310
Does the best job if we covering
the input model with the fewest

bda32352-a5ee-4f54-a17e-dc796256864d/5561-1
00:25:26.310 --> 00:25:29.498
number of samples and notice the
number of samples downhill is

bda32352-a5ee-4f54-a17e-dc796256864d/5561-2
00:25:29.498 --> 00:25:32.180
log scale and the answer is
there crossfading winds.

bda32352-a5ee-4f54-a17e-dc796256864d/5574-0
00:25:32.310 --> 00:25:35.638
Crossfading recovers the input
model more accurately with fuel

bda32352-a5ee-4f54-a17e-dc796256864d/5574-1
00:25:35.638 --> 00:25:36.060
samples.

bda32352-a5ee-4f54-a17e-dc796256864d/5586-0
00:25:36.610 --> 00:25:41.350
So bookoo, I think we solved the
first problem.

bda32352-a5ee-4f54-a17e-dc796256864d/5609-0
00:25:41.400 --> 00:25:44.632
I think you know I can go to my
friend just now and be like, OK,

bda32352-a5ee-4f54-a17e-dc796256864d/5609-1
00:25:44.632 --> 00:25:46.670
like this problem is not so bad
anymore.

bda32352-a5ee-4f54-a17e-dc796256864d/5623-0
00:25:46.680 --> 00:25:48.993
You can go do a regular
earthquake model like solving

bda32352-a5ee-4f54-a17e-dc796256864d/5623-1
00:25:48.993 --> 00:25:50.020
for the request sources.

bda32352-a5ee-4f54-a17e-dc796256864d/5643-0
00:25:52.160 --> 00:25:55.349
On your, you know, work station
in MATLAB and I'll just take you

bda32352-a5ee-4f54-a17e-dc796256864d/5643-1
00:25:55.349 --> 00:25:55.790
a minute.

bda32352-a5ee-4f54-a17e-dc796256864d/5649-0
00:25:55.800 --> 00:25:56.260
It'll be fine.

bda32352-a5ee-4f54-a17e-dc796256864d/5669-0
00:25:57.720 --> 00:26:00.410
Also, I think it's always the
problem of doing it.

bda32352-a5ee-4f54-a17e-dc796256864d/5705-0
00:26:00.420 --> 00:26:04.442
Doing a submittal resolution run
and using big data because as it

bda32352-a5ee-4f54-a17e-dc796256864d/5705-1
00:26:04.442 --> 00:26:08.281
turns out, I'm when you write
the problem this way, there's no

bda32352-a5ee-4f54-a17e-dc796256864d/5705-2
00:26:08.281 --> 00:26:10.170
data likelihood in the problem.

bda32352-a5ee-4f54-a17e-dc796256864d/5708-0
00:26:10.540 --> 00:26:11.570
There's no forward model.

bda32352-a5ee-4f54-a17e-dc796256864d/5714-0
00:26:11.640 --> 00:26:12.390
There's no data.

bda32352-a5ee-4f54-a17e-dc796256864d/5724-0
00:26:12.440 --> 00:26:14.530
There's no misfit between the
data and the predictions.

bda32352-a5ee-4f54-a17e-dc796256864d/5739-0
00:26:14.780 --> 00:26:16.726
There's nothing that came as
whether or not you have 10

bda32352-a5ee-4f54-a17e-dc796256864d/5739-1
00:26:16.726 --> 00:26:17.420
million data points.

bda32352-a5ee-4f54-a17e-dc796256864d/5820-0
00:26:19.590 --> 00:26:23.506
Umm, so once again my normally
if you're trying to stimulate

bda32352-a5ee-4f54-a17e-dc796256864d/5820-1
00:26:23.506 --> 00:26:27.422
the posterior PDF you have to
draw some value for your model

bda32352-a5ee-4f54-a17e-dc796256864d/5820-2
00:26:27.422 --> 00:26:31.273
parameters, calculate the prior
probability associated with

bda32352-a5ee-4f54-a17e-dc796256864d/5820-3
00:26:31.273 --> 00:26:35.253
those values and then also run
the forward model to get a set

bda32352-a5ee-4f54-a17e-dc796256864d/5820-4
00:26:35.253 --> 00:26:39.297
of predictions to calculate the
misfits your data to calculate

bda32352-a5ee-4f54-a17e-dc796256864d/5820-5
00:26:39.297 --> 00:26:43.533
the data likelihood and the more
data you have the more expensive

bda32352-a5ee-4f54-a17e-dc796256864d/5820-6
00:26:43.533 --> 00:26:44.560
that's gonna be.

bda32352-a5ee-4f54-a17e-dc796256864d/5850-0
00:26:45.360 --> 00:26:49.415
But in Crossfading to calculate
the posterior PDF, we calculate

bda32352-a5ee-4f54-a17e-dc796256864d/5850-1
00:26:49.415 --> 00:26:53.407
still the prior PDF, but then
also the conjugate posterior and

bda32352-a5ee-4f54-a17e-dc796256864d/5850-2
00:26:53.407 --> 00:26:54.610
the conjugate file.

bda32352-a5ee-4f54-a17e-dc796256864d/5861-0
00:26:54.860 --> 00:26:57.130
Those are all functions of model
parameters.

bda32352-a5ee-4f54-a17e-dc796256864d/5879-0
00:26:57.240 --> 00:26:59.934
They do not contain anything
having to do with the data or

bda32352-a5ee-4f54-a17e-dc796256864d/5879-1
00:26:59.934 --> 00:27:00.390
the model.

bda32352-a5ee-4f54-a17e-dc796256864d/5882-0
00:27:00.520 --> 00:27:01.370
Any information?

bda32352-a5ee-4f54-a17e-dc796256864d/5886-0
00:27:01.380 --> 00:27:01.590
Essay.

bda32352-a5ee-4f54-a17e-dc796256864d/5906-0
00:27:01.600 --> 00:27:04.705
But the data in the model was
incorporated analytically into

bda32352-a5ee-4f54-a17e-dc796256864d/5906-1
00:27:04.705 --> 00:27:06.130
the conjugate posterior PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/5915-0
00:27:06.200 --> 00:27:08.020
No likelihood, no data, no
forward model.

bda32352-a5ee-4f54-a17e-dc796256864d/5939-0
00:27:08.180 --> 00:27:10.759
The computational cost across
fading never increases, no

bda32352-a5ee-4f54-a17e-dc796256864d/5939-1
00:27:10.759 --> 00:27:12.930
matter how many data are used
and on the right.

bda32352-a5ee-4f54-a17e-dc796256864d/5973-0
00:27:12.940 --> 00:27:17.223
This is simply a plot where I
show how much time it takes to

bda32352-a5ee-4f54-a17e-dc796256864d/5973-1
00:27:17.223 --> 00:27:21.506
run the calculate the posterior
PDF for the same model for a

bda32352-a5ee-4f54-a17e-dc796256864d/5973-2
00:27:21.506 --> 00:27:22.910
simple linear model.

bda32352-a5ee-4f54-a17e-dc796256864d/6014-0
00:27:23.920 --> 00:27:28.021
Umm for the for a simple data
likelihood d -, G times data CD

bda32352-a5ee-4f54-a17e-dc796256864d/6014-1
00:27:28.021 --> 00:27:32.254
invoice d -, G times Theta and
the cost of that is gonna depend

bda32352-a5ee-4f54-a17e-dc796256864d/6014-2
00:27:32.254 --> 00:27:35.230
on whether or not CBD is a full
rank matrix.

bda32352-a5ee-4f54-a17e-dc796256864d/6086-0
00:27:35.240 --> 00:27:38.039
So this is a matrix vector
multiply, or whether at the

bda32352-a5ee-4f54-a17e-dc796256864d/6086-1
00:27:38.039 --> 00:27:41.295
cheapest side it's a nice topic
matrix, so it's just a scale of

bda32352-a5ee-4f54-a17e-dc796256864d/6086-2
00:27:41.295 --> 00:27:44.298
Sigma squared and anything in
between will be something in

bda32352-a5ee-4f54-a17e-dc796256864d/6086-3
00:27:44.298 --> 00:27:47.249
between and as the number of
observations increases, that

bda32352-a5ee-4f54-a17e-dc796256864d/6086-4
00:27:47.249 --> 00:27:50.200
number is gonna get larger and
larger to compute, because

bda32352-a5ee-4f54-a17e-dc796256864d/6086-5
00:27:50.200 --> 00:27:53.100
that's gonna be more and more
floating point operations.

bda32352-a5ee-4f54-a17e-dc796256864d/6118-0
00:27:53.830 --> 00:27:56.612
But the time it takes to compute
cross fading level increases

bda32352-a5ee-4f54-a17e-dc796256864d/6118-1
00:27:56.612 --> 00:27:59.124
because there's nothing
involving data or forward model

bda32352-a5ee-4f54-a17e-dc796256864d/6118-2
00:27:59.124 --> 00:28:01.680
in the problem when you address
it through cross fading.

bda32352-a5ee-4f54-a17e-dc796256864d/6126-0
00:28:04.660 --> 00:28:05.760
So what do we have?

bda32352-a5ee-4f54-a17e-dc796256864d/6141-0
00:28:05.820 --> 00:28:08.684
A very efficient sampling method
does not require evaluating the

bda32352-a5ee-4f54-a17e-dc796256864d/6141-1
00:28:08.684 --> 00:28:09.300
forward model.

bda32352-a5ee-4f54-a17e-dc796256864d/6145-0
00:28:09.310 --> 00:28:09.930
The data misfit.

bda32352-a5ee-4f54-a17e-dc796256864d/6152-0
00:28:10.620 --> 00:28:11.730
What is it good for?

bda32352-a5ee-4f54-a17e-dc796256864d/6167-0
00:28:11.840 --> 00:28:14.399
And you'll probably thinking
then your models and the answer

bda32352-a5ee-4f54-a17e-dc796256864d/6167-1
00:28:14.399 --> 00:28:14.650
is no.

bda32352-a5ee-4f54-a17e-dc796256864d/6182-0
00:28:14.660 --> 00:28:16.510
I mean, yes, we just used it for
all the new model.

bda32352-a5ee-4f54-a17e-dc796256864d/6221-0
00:28:16.520 --> 00:28:18.955
You can use it for the new
models, but this actually

bda32352-a5ee-4f54-a17e-dc796256864d/6221-1
00:28:18.955 --> 00:28:21.803
nothing about this that care is
about whether you're model is

bda32352-a5ee-4f54-a17e-dc796256864d/6221-2
00:28:21.803 --> 00:28:24.559
linear, whether you used normal
statistics or anything like

bda32352-a5ee-4f54-a17e-dc796256864d/6221-3
00:28:24.559 --> 00:28:25.110
that, right?

bda32352-a5ee-4f54-a17e-dc796256864d/6251-0
00:28:25.240 --> 00:28:29.368
The question is just, does there
exist a posterior PDF that you

bda32352-a5ee-4f54-a17e-dc796256864d/6251-1
00:28:29.368 --> 00:28:33.367
can simulate directly so that
you have something to start the

bda32352-a5ee-4f54-a17e-dc796256864d/6251-2
00:28:33.367 --> 00:28:34.270
sampling from?

bda32352-a5ee-4f54-a17e-dc796256864d/6288-0
00:28:34.620 --> 00:28:37.573
Any likelihood for which this
the post you a PDF that can be

bda32352-a5ee-4f54-a17e-dc796256864d/6288-1
00:28:37.573 --> 00:28:40.477
directly simulated and thus used
as the starting PDF across

bda32352-a5ee-4f54-a17e-dc796256864d/6288-2
00:28:40.477 --> 00:28:43.430
fading and typically this means
the existence of a conjugate

bda32352-a5ee-4f54-a17e-dc796256864d/6288-3
00:28:43.430 --> 00:28:43.720
trial?

bda32352-a5ee-4f54-a17e-dc796256864d/6314-0
00:28:44.820 --> 00:28:47.505
Umm, so Crossfading won't work
for every problem, but it works

bda32352-a5ee-4f54-a17e-dc796256864d/6314-1
00:28:47.505 --> 00:28:49.890
for a larger class of problems
than you probably think.

bda32352-a5ee-4f54-a17e-dc796256864d/6320-0
00:28:50.320 --> 00:28:51.250
I mean, think of it this way.

bda32352-a5ee-4f54-a17e-dc796256864d/6339-0
00:28:51.760 --> 00:28:54.096
You know, based on the place
basically independently

bda32352-a5ee-4f54-a17e-dc796256864d/6339-1
00:28:54.096 --> 00:28:56.210
developed probabilistic
influence in the 1700s.

bda32352-a5ee-4f54-a17e-dc796256864d/6367-0
00:28:57.080 --> 00:29:00.480
You know MCMC Foster PO in the
1953 metropolis at all PayPal

bda32352-a5ee-4f54-a17e-dc796256864d/6367-1
00:29:00.480 --> 00:29:02.430
mobile people doing for 200
years.

bda32352-a5ee-4f54-a17e-dc796256864d/6388-0
00:29:02.440 --> 00:29:05.057
In between they were doing
analytical solutions and there's

bda32352-a5ee-4f54-a17e-dc796256864d/6388-1
00:29:05.057 --> 00:29:07.150
a lot of analytical solutions
out there, right?

bda32352-a5ee-4f54-a17e-dc796256864d/6407-0
00:29:07.300 --> 00:29:09.238
So if you wanna do linear
regression then you'll

bda32352-a5ee-4f54-a17e-dc796256864d/6407-1
00:29:09.238 --> 00:29:10.700
likelihood is a normal
distribution.

bda32352-a5ee-4f54-a17e-dc796256864d/6425-0
00:29:10.710 --> 00:29:13.125
That's the problem we just did
and the conjugate file was a

bda32352-a5ee-4f54-a17e-dc796256864d/6425-1
00:29:13.125 --> 00:29:13.930
normal distribution.

bda32352-a5ee-4f54-a17e-dc796256864d/6460-0
00:29:14.240 --> 00:29:16.584
If you want to estimate the B
value of an earthquake catalog,

bda32352-a5ee-4f54-a17e-dc796256864d/6460-1
00:29:16.584 --> 00:29:18.890
then you'll likelihood as an
exponential and the content you

bda32352-a5ee-4f54-a17e-dc796256864d/6460-2
00:29:18.890 --> 00:29:20.250
could file is a gamma
distribution.

bda32352-a5ee-4f54-a17e-dc796256864d/6479-0
00:29:21.250 --> 00:29:24.293
If you are studying for some
processes then your country file

bda32352-a5ee-4f54-a17e-dc796256864d/6479-1
00:29:24.293 --> 00:29:25.520
still gamma distribution.

bda32352-a5ee-4f54-a17e-dc796256864d/6526-0
00:29:25.710 --> 00:29:28.387
If you're studying binomial
processes, then your conjugate

bda32352-a5ee-4f54-a17e-dc796256864d/6526-1
00:29:28.387 --> 00:29:31.200
prior is a beta distribution
right before they were computers

bda32352-a5ee-4f54-a17e-dc796256864d/6526-2
00:29:31.200 --> 00:29:34.150
to do the mail integration, they
will integral tables and before

bda32352-a5ee-4f54-a17e-dc796256864d/6526-3
00:29:34.150 --> 00:29:36.963
they will computers to do MCMC,
they will tables of conjugate

bda32352-a5ee-4f54-a17e-dc796256864d/6526-4
00:29:36.963 --> 00:29:37.280
priors.

bda32352-a5ee-4f54-a17e-dc796256864d/6543-0
00:29:37.570 --> 00:29:40.585
So if you wanna do this,
basically Wikipedia and Google

bda32352-a5ee-4f54-a17e-dc796256864d/6543-1
00:29:40.585 --> 00:29:41.500
are your friends.

bda32352-a5ee-4f54-a17e-dc796256864d/6568-0
00:29:42.040 --> 00:29:44.907
Look up and see if there exists
a conjugate prior to the problem

bda32352-a5ee-4f54-a17e-dc796256864d/6568-1
00:29:44.907 --> 00:29:45.480
you wanna do.

bda32352-a5ee-4f54-a17e-dc796256864d/6578-0
00:29:45.490 --> 00:29:47.290
In fact, it's still an active
area of research.

bda32352-a5ee-4f54-a17e-dc796256864d/6603-0
00:29:47.300 --> 00:29:50.017
Still, people still churning out
papers about this because they

bda32352-a5ee-4f54-a17e-dc796256864d/6603-1
00:29:50.017 --> 00:29:51.800
just so useful when it comes to
the file.

bda32352-a5ee-4f54-a17e-dc796256864d/6608-0
00:29:51.810 --> 00:29:52.200
Does exist?

bda32352-a5ee-4f54-a17e-dc796256864d/6622-0
00:29:53.930 --> 00:29:55.630
Do we have a new magic sample
though?

bda32352-a5ee-4f54-a17e-dc796256864d/6624-0
00:29:55.680 --> 00:29:57.170
It is so efficient.

bda32352-a5ee-4f54-a17e-dc796256864d/6653-0
00:29:57.310 --> 00:30:00.757
It works for big data and then
it had to go and ask another

bda32352-a5ee-4f54-a17e-dc796256864d/6653-1
00:30:00.757 --> 00:30:04.261
question and that question was
what about the arrows and the

bda32352-a5ee-4f54-a17e-dc796256864d/6653-2
00:30:04.261 --> 00:30:05.410
model design, right?

bda32352-a5ee-4f54-a17e-dc796256864d/6677-0
00:30:05.420 --> 00:30:09.812
And Bayesian analysis is called
the model prediction errors and

bda32352-a5ee-4f54-a17e-dc796256864d/6677-1
00:30:09.812 --> 00:30:13.860
other fields that usually
follows epistemic errors. Right?

bda32352-a5ee-4f54-a17e-dc796256864d/6743-0
00:30:13.930 --> 00:30:18.312
So so like you might be used to
thinking of inverse problems As

bda32352-a5ee-4f54-a17e-dc796256864d/6743-1
00:30:18.312 --> 00:30:22.694
for example, if it's d = g * M,
You're usually used to think of

bda32352-a5ee-4f54-a17e-dc796256864d/6743-2
00:30:22.694 --> 00:30:27.008
it d * g * M times epsilon, but
in bayland it's your data plus

bda32352-a5ee-4f54-a17e-dc796256864d/6743-3
00:30:27.008 --> 00:30:31.458
the arrows on your observations
is equal to your prediction plus

bda32352-a5ee-4f54-a17e-dc796256864d/6743-4
00:30:31.458 --> 00:30:33.580
the errors and your prediction.

bda32352-a5ee-4f54-a17e-dc796256864d/6783-0
00:30:33.640 --> 00:30:36.961
The difference between what
y'all model predicted for your

bda32352-a5ee-4f54-a17e-dc796256864d/6783-1
00:30:36.961 --> 00:30:40.338
for your model parameters and
what it should have predicted

bda32352-a5ee-4f54-a17e-dc796256864d/6783-2
00:30:40.338 --> 00:30:43.940
for those model parameters, and
so then we apply Bayes theorem.

bda32352-a5ee-4f54-a17e-dc796256864d/6819-0
00:30:44.210 --> 00:30:48.130
If it was again the simple
linear problem with the simple

bda32352-a5ee-4f54-a17e-dc796256864d/6819-1
00:30:48.130 --> 00:30:52.523
exponential likelihood function,
the covariance matrix there was

bda32352-a5ee-4f54-a17e-dc796256864d/6819-2
00:30:52.523 --> 00:30:56.240
not the covariance of the arrows
on your observations.

bda32352-a5ee-4f54-a17e-dc796256864d/6854-0
00:30:56.250 --> 00:30:59.864
It's actually the sum of the
errors of your observations and

bda32352-a5ee-4f54-a17e-dc796256864d/6854-1
00:30:59.864 --> 00:31:03.359
your prediction arrows, and
those prediction arrows can be

bda32352-a5ee-4f54-a17e-dc796256864d/6854-2
00:31:03.359 --> 00:31:06.380
large amplitude and they can be
highly correlated.

bda32352-a5ee-4f54-a17e-dc796256864d/6883-0
00:31:06.390 --> 00:31:09.960
So if, as we often do, we only
consider observational errors,

bda32352-a5ee-4f54-a17e-dc796256864d/6883-1
00:31:09.960 --> 00:31:13.357
we are really, really miss
estimating the arrow structural

bda32352-a5ee-4f54-a17e-dc796256864d/6883-2
00:31:13.357 --> 00:31:14.220
in our problem.

bda32352-a5ee-4f54-a17e-dc796256864d/6916-0
00:31:14.920 --> 00:31:18.331
So to get a kind of a intuition
about this, let's play a little

bda32352-a5ee-4f54-a17e-dc796256864d/6916-1
00:31:18.331 --> 00:31:21.315
game with the Tohoku off Craig
and what I did here is I

bda32352-a5ee-4f54-a17e-dc796256864d/6916-2
00:31:21.315 --> 00:31:23.020
generated 500,000 source models.

bda32352-a5ee-4f54-a17e-dc796256864d/6923-0
00:31:23.030 --> 00:31:24.720
They're basically just white
noise.

bda32352-a5ee-4f54-a17e-dc796256864d/6944-0
00:31:24.850 --> 00:31:27.888
There's a back zip constraint,
but otherwise there's no

bda32352-a5ee-4f54-a17e-dc796256864d/6944-1
00:31:27.888 --> 00:31:30.600
constraint on what direction
each patch slips in.

bda32352-a5ee-4f54-a17e-dc796256864d/6952-0
00:31:31.510 --> 00:31:33.260
How much slip is on each patch?
Right?

bda32352-a5ee-4f54-a17e-dc796256864d/6983-0
00:31:33.330 --> 00:31:36.601
The source is just random values
and then I calculated the

bda32352-a5ee-4f54-a17e-dc796256864d/6983-1
00:31:36.601 --> 00:31:39.484
predictions for this 500,000
step models and then I

bda32352-a5ee-4f54-a17e-dc796256864d/6983-2
00:31:39.484 --> 00:31:42.200
calculated the correlation of
those predictions.

bda32352-a5ee-4f54-a17e-dc796256864d/7008-0
00:31:42.450 --> 00:31:45.755
So any signal you see anything
coherent you see has nothing to

bda32352-a5ee-4f54-a17e-dc796256864d/7008-1
00:31:45.755 --> 00:31:48.640
do with the source, cause the
software is white noise.

bda32352-a5ee-4f54-a17e-dc796256864d/7059-0
00:31:49.040 --> 00:31:52.328
Anything coherent you see is the
model design itself, and boy is

bda32352-a5ee-4f54-a17e-dc796256864d/7059-1
00:31:52.328 --> 00:31:55.414
a coherent because you know,
once you say there's a back zip

bda32352-a5ee-4f54-a17e-dc796256864d/7059-2
00:31:55.414 --> 00:31:58.247
constraint, then there's
absolutely no step you can put

bda32352-a5ee-4f54-a17e-dc796256864d/7059-3
00:31:58.247 --> 00:32:01.130
on the fault that doesn't make
consume move to the east.

bda32352-a5ee-4f54-a17e-dc796256864d/7106-0
00:32:01.930 --> 00:32:03.996
Once you pick a dip for your
four geometry, there's

bda32352-a5ee-4f54-a17e-dc796256864d/7106-1
00:32:03.996 --> 00:32:06.419
absolutely nothing you can do
that doesn't make a hinge line

bda32352-a5ee-4f54-a17e-dc796256864d/7106-2
00:32:06.419 --> 00:32:08.682
in a certain location and
everything on one side of that

bda32352-a5ee-4f54-a17e-dc796256864d/7106-3
00:32:08.682 --> 00:32:10.787
hinge line goes up and
everything on the other side,

bda32352-a5ee-4f54-a17e-dc796256864d/7106-4
00:32:10.787 --> 00:32:11.780
the hinge line goes down.

bda32352-a5ee-4f54-a17e-dc796256864d/7122-0
00:32:12.810 --> 00:32:15.888
If you look at wave form data,
these are five tsunami records

bda32352-a5ee-4f54-a17e-dc796256864d/7122-1
00:32:15.888 --> 00:32:16.880
from the earthquake.

bda32352-a5ee-4f54-a17e-dc796256864d/7133-0
00:32:17.610 --> 00:32:19.540
Then you're just adding time to
the problem, right?

bda32352-a5ee-4f54-a17e-dc796256864d/7152-0
00:32:19.550 --> 00:32:22.689
So forced each record is very
correlated with itself because

bda32352-a5ee-4f54-a17e-dc796256864d/7152-1
00:32:22.689 --> 00:32:23.460
they are waved.

bda32352-a5ee-4f54-a17e-dc796256864d/7174-0
00:32:23.470 --> 00:32:26.113
So each sample knows what
happened with the sample before

bda32352-a5ee-4f54-a17e-dc796256864d/7174-1
00:32:26.113 --> 00:32:28.300
and after it, and from one
station to the next.

bda32352-a5ee-4f54-a17e-dc796256864d/7207-0
00:32:28.310 --> 00:32:30.501
They'll be very highly
correlated because whatever you

bda32352-a5ee-4f54-a17e-dc796256864d/7207-1
00:32:30.501 --> 00:32:32.811
predict for one station is
basically going to be the same

bda32352-a5ee-4f54-a17e-dc796256864d/7207-2
00:32:32.811 --> 00:32:35.200
thing you predicted the next
station, but shift it in time.

bda32352-a5ee-4f54-a17e-dc796256864d/7221-0
00:32:36.730 --> 00:32:39.120
None of this observational
signals related to the

bda32352-a5ee-4f54-a17e-dc796256864d/7221-1
00:32:39.120 --> 00:32:39.980
earthquake source.

bda32352-a5ee-4f54-a17e-dc796256864d/7229-0
00:32:39.990 --> 00:32:41.200
Again, the source was white
noise.

bda32352-a5ee-4f54-a17e-dc796256864d/7242-0
00:32:41.410 --> 00:32:43.520
All of the signal is your model
design, right?

bda32352-a5ee-4f54-a17e-dc796256864d/7252-0
00:32:43.530 --> 00:32:44.820
It's your choice of velocity
model.

bda32352-a5ee-4f54-a17e-dc796256864d/7275-0
00:32:44.830 --> 00:32:47.749
Your choice of four geometry and
of course you're more design

bda32352-a5ee-4f54-a17e-dc796256864d/7275-1
00:32:47.749 --> 00:32:49.820
will be wrong because all models
are wrong.

bda32352-a5ee-4f54-a17e-dc796256864d/7281-0
00:32:49.870 --> 00:32:51.610
So we all kinda doomed.

bda32352-a5ee-4f54-a17e-dc796256864d/7291-0
00:32:52.360 --> 00:32:54.670
I'm and people have been working
on this right.

bda32352-a5ee-4f54-a17e-dc796256864d/7299-0
00:32:54.680 --> 00:32:56.890
This is a really important field
of research.

bda32352-a5ee-4f54-a17e-dc796256864d/7304-0
00:32:57.210 --> 00:32:58.890
I'd say there's basically 2
approaches.

bda32352-a5ee-4f54-a17e-dc796256864d/7331-0
00:32:59.000 --> 00:33:02.097
One is kind of a parametric
approach where you say like ohh

bda32352-a5ee-4f54-a17e-dc796256864d/7331-1
00:33:02.097 --> 00:33:04.780
I have some other error source
that has some Sigma.

bda32352-a5ee-4f54-a17e-dc796256864d/7338-0
00:33:04.790 --> 00:33:06.670
I don't know it has some
correlation link.

bda32352-a5ee-4f54-a17e-dc796256864d/7367-0
00:33:06.680 --> 00:33:08.735
They don't know and you just
solve for those numbers at the

bda32352-a5ee-4f54-a17e-dc796256864d/7367-1
00:33:08.735 --> 00:33:10.550
same time that you're solving
for your source model.

bda32352-a5ee-4f54-a17e-dc796256864d/7381-0
00:33:11.380 --> 00:33:14.336
The other one is, for example
Zach do Patel and they were

bda32352-a5ee-4f54-a17e-dc796256864d/7381-1
00:33:14.336 --> 00:33:14.590
gone.

bda32352-a5ee-4f54-a17e-dc796256864d/7448-0
00:33:14.600 --> 00:33:18.313
I've been working on this
perturbation approaches where

bda32352-a5ee-4f54-a17e-dc796256864d/7448-1
00:33:18.313 --> 00:33:22.556
you calculate the coveo, the the
the predictions that you would

bda32352-a5ee-4f54-a17e-dc796256864d/7448-2
00:33:22.556 --> 00:33:26.667
get from your model if you told
the elastic structure, or you

bda32352-a5ee-4f54-a17e-dc796256864d/7448-3
00:33:26.667 --> 00:33:30.645
perturb the fault geometry and
then the covariance of those

bda32352-a5ee-4f54-a17e-dc796256864d/7448-4
00:33:30.645 --> 00:33:35.020
predictions, and that's what you
stick into your data likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/7463-0
00:33:35.110 --> 00:33:37.627
But of course, in order to get
those predictions, you have to

bda32352-a5ee-4f54-a17e-dc796256864d/7463-1
00:33:37.627 --> 00:33:38.520
know the source model.

bda32352-a5ee-4f54-a17e-dc796256864d/7504-0
00:33:38.590 --> 00:33:41.950
So again, you have to kind of
update it through the sampling

bda32352-a5ee-4f54-a17e-dc796256864d/7504-1
00:33:41.950 --> 00:33:45.254
process and anyway you end up
having to solve for something

bda32352-a5ee-4f54-a17e-dc796256864d/7504-2
00:33:45.254 --> 00:33:48.779
during the sampling process and
with crossfading, we don't have

bda32352-a5ee-4f54-a17e-dc796256864d/7504-3
00:33:48.779 --> 00:33:50.210
a data likelihood anymore.

bda32352-a5ee-4f54-a17e-dc796256864d/7583-0
00:33:50.500 --> 00:33:54.035
So I went to my friend Matt and
I said, well, math, how do I

bda32352-a5ee-4f54-a17e-dc796256864d/7583-1
00:33:54.035 --> 00:33:57.570
account for the arrows in the
model design while Phosphating

bda32352-a5ee-4f54-a17e-dc796256864d/7583-2
00:33:57.570 --> 00:34:01.220
and Matt said, well, you can't,
you don't have a likelihood of

bda32352-a5ee-4f54-a17e-dc796256864d/7583-3
00:34:01.220 --> 00:34:04.812
ohh I'd covariance matrix you
update and it's like but math I

bda32352-a5ee-4f54-a17e-dc796256864d/7583-4
00:34:04.812 --> 00:34:08.057
have to include the prediction
error like it's the most

bda32352-a5ee-4f54-a17e-dc796256864d/7583-5
00:34:08.057 --> 00:34:11.070
important thing and math was
like, well, you can't.

bda32352-a5ee-4f54-a17e-dc796256864d/7587-0
00:34:11.080 --> 00:34:12.390
You wanted the date on the
forward model.

bda32352-a5ee-4f54-a17e-dc796256864d/7589-0
00:34:12.400 --> 00:34:12.750
Gone.

bda32352-a5ee-4f54-a17e-dc796256864d/7592-0
00:34:12.800 --> 00:34:13.430
They're gone.

bda32352-a5ee-4f54-a17e-dc796256864d/7620-0
00:34:13.440 --> 00:34:16.587
You can't account for hours in
the photo model without a

bda32352-a5ee-4f54-a17e-dc796256864d/7620-1
00:34:16.587 --> 00:34:19.899
forward model, and I said, but
man, it's the most important

bda32352-a5ee-4f54-a17e-dc796256864d/7620-2
00:34:19.899 --> 00:34:20.230
thing.

bda32352-a5ee-4f54-a17e-dc796256864d/7633-0
00:34:21.080 --> 00:34:23.334
And my friend Matt said, well,
have you considered solving for

bda32352-a5ee-4f54-a17e-dc796256864d/7633-1
00:34:23.334 --> 00:34:23.870
the earthquake?

bda32352-a5ee-4f54-a17e-dc796256864d/7693-0
00:34:23.870 --> 00:34:27.552
Rupture, given all the potential
model designs and I said math,

bda32352-a5ee-4f54-a17e-dc796256864d/7693-1
00:34:27.552 --> 00:34:30.946
we can barely solve for the
earthquake sauce like we can't

bda32352-a5ee-4f54-a17e-dc796256864d/7693-2
00:34:30.946 --> 00:34:34.283
solve for the sauce and the
elastic structure and the 4th

bda32352-a5ee-4f54-a17e-dc796256864d/7693-3
00:34:34.283 --> 00:34:37.562
geometry and math is like no,
no, no, not the earthquake

bda32352-a5ee-4f54-a17e-dc796256864d/7693-4
00:34:37.562 --> 00:34:39.230
rupture and the model design.

bda32352-a5ee-4f54-a17e-dc796256864d/7705-0
00:34:39.240 --> 00:34:43.463
The earthquake webshow given, or
the potential model designs, and

bda32352-a5ee-4f54-a17e-dc796256864d/7705-1
00:34:43.463 --> 00:34:43.910
I said.

bda32352-a5ee-4f54-a17e-dc796256864d/7716-0
00:34:44.690 --> 00:34:48.800
Ohh so here was what math meant.

bda32352-a5ee-4f54-a17e-dc796256864d/7734-0
00:34:49.870 --> 00:34:52.911
You know, every time you fit a
model to data, you also make a

bda32352-a5ee-4f54-a17e-dc796256864d/7734-1
00:34:52.911 --> 00:34:53.940
bunch of assumptions.

bda32352-a5ee-4f54-a17e-dc796256864d/7738-0
00:34:54.590 --> 00:34:56.000
Make different assumptions.

bda32352-a5ee-4f54-a17e-dc796256864d/7765-0
00:34:56.010 --> 00:34:59.619
Get a different answer, and of
course, in Bayesian inland your

bda32352-a5ee-4f54-a17e-dc796256864d/7765-1
00:34:59.619 --> 00:35:01.680
answer is not a number, it's a
PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/7797-0
00:35:01.750 --> 00:35:05.556
So you can think of these four
different PDFs as PDFs of the

bda32352-a5ee-4f54-a17e-dc796256864d/7797-1
00:35:05.556 --> 00:35:09.236
thing that I wanted to know
under different assumptions of

bda32352-a5ee-4f54-a17e-dc796256864d/7797-2
00:35:09.236 --> 00:35:11.170
something that I had to assume.

bda32352-a5ee-4f54-a17e-dc796256864d/7822-0
00:35:12.680 --> 00:35:15.221
So I wanted to know the step
right on this fault, but in

bda32352-a5ee-4f54-a17e-dc796256864d/7822-1
00:35:15.221 --> 00:35:17.450
order to do that I had to assume
a locking depth.

bda32352-a5ee-4f54-a17e-dc796256864d/7848-0
00:35:17.800 --> 00:35:20.324
I wanted to know the hypocenter
of this earthquake, but in order

bda32352-a5ee-4f54-a17e-dc796256864d/7848-1
00:35:20.324 --> 00:35:22.070
to do that I had to assume a
velocity model.

bda32352-a5ee-4f54-a17e-dc796256864d/7872-0
00:35:22.580 --> 00:35:25.754
I wanted to, you know, solve for
defamation based on

bda32352-a5ee-4f54-a17e-dc796256864d/7872-1
00:35:25.754 --> 00:35:27.670
interferogram or some GNSS data.

bda32352-a5ee-4f54-a17e-dc796256864d/7893-0
00:35:27.760 --> 00:35:32.600
But in a field, grams have an
arbitrary number of 2π phase

bda32352-a5ee-4f54-a17e-dc796256864d/7893-1
00:35:32.600 --> 00:35:33.830
cycles in them.

bda32352-a5ee-4f54-a17e-dc796256864d/7915-0
00:35:34.100 --> 00:35:37.854
GNS data have reference frame
jiggle right and I have to make

bda32352-a5ee-4f54-a17e-dc796256864d/7915-1
00:35:37.854 --> 00:35:40.880
some assumption for that in
order to do my model.

bda32352-a5ee-4f54-a17e-dc796256864d/7921-0
00:35:41.740 --> 00:35:42.850
Make different assumptions.

bda32352-a5ee-4f54-a17e-dc796256864d/7924-0
00:35:42.920 --> 00:35:43.730
Get different answers.

bda32352-a5ee-4f54-a17e-dc796256864d/7927-0
00:35:44.730 --> 00:35:45.100
Umm.

bda32352-a5ee-4f54-a17e-dc796256864d/7980-0
00:35:45.670 --> 00:35:49.051
All right, all you could think
of each answer as being a slice

bda32352-a5ee-4f54-a17e-dc796256864d/7980-1
00:35:49.051 --> 00:35:52.377
through a joint distribution of
the things you wanted to know

bda32352-a5ee-4f54-a17e-dc796256864d/7980-2
00:35:52.377 --> 00:35:55.650
and the things you had to assume
or with math would say each

bda32352-a5ee-4f54-a17e-dc796256864d/7980-3
00:35:55.650 --> 00:35:58.440
Ansel is a posterior PDF for
different model class.

bda32352-a5ee-4f54-a17e-dc796256864d/7994-0
00:36:00.590 --> 00:36:03.330
But this joint distribution is
also not what you want.

bda32352-a5ee-4f54-a17e-dc796256864d/8023-0
00:36:03.570 --> 00:36:06.286
Really what you wanna do is to
integrate over all the model

bda32352-a5ee-4f54-a17e-dc796256864d/8023-1
00:36:06.286 --> 00:36:08.910
classes to get the run in
version to rule them all right.

bda32352-a5ee-4f54-a17e-dc796256864d/8045-0
00:36:08.920 --> 00:36:11.245
This is the invoice model that
knows all the different

bda32352-a5ee-4f54-a17e-dc796256864d/8045-1
00:36:11.245 --> 00:36:13.950
assumptions you could have made
and how they affect the answer.

bda32352-a5ee-4f54-a17e-dc796256864d/8049-0
00:36:13.960 --> 00:36:15.040
You could have gotten right.

bda32352-a5ee-4f54-a17e-dc796256864d/8062-0
00:36:15.050 --> 00:36:18.240
It's the step rate given all
possible locking depths.

bda32352-a5ee-4f54-a17e-dc796256864d/8096-0
00:36:18.250 --> 00:36:22.693
It's the hypothetical, given all
possible velocity models, and in

bda32352-a5ee-4f54-a17e-dc796256864d/8096-1
00:36:22.693 --> 00:36:26.934
this picture it's this black PDF
in the back wall that you get

bda32352-a5ee-4f54-a17e-dc796256864d/8096-2
00:36:26.934 --> 00:36:29.020
from integrating the joint PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/8099-0
00:36:29.150 --> 00:36:29.570
Oval.

bda32352-a5ee-4f54-a17e-dc796256864d/8105-0
00:36:29.830 --> 00:36:30.810
Ohh model designs.

bda32352-a5ee-4f54-a17e-dc796256864d/8139-0
00:36:31.800 --> 00:36:34.682
Umm, but it turns out that you
don't actually have to do that

bda32352-a5ee-4f54-a17e-dc796256864d/8139-1
00:36:34.682 --> 00:36:37.425
to get that answer, because you
can approximate it by just

bda32352-a5ee-4f54-a17e-dc796256864d/8139-2
00:36:37.425 --> 00:36:39.470
taking a bunch of different
answers, right?

bda32352-a5ee-4f54-a17e-dc796256864d/8185-0
00:36:39.480 --> 00:36:41.817
Like all four answers that we
computed for a different

bda32352-a5ee-4f54-a17e-dc796256864d/8185-1
00:36:41.817 --> 00:36:44.452
assumptions and that's taking
the weighted sum and that gives

bda32352-a5ee-4f54-a17e-dc796256864d/8185-2
00:36:44.452 --> 00:36:47.171
you the green line, which is a
pretty good approximation to the

bda32352-a5ee-4f54-a17e-dc796256864d/8185-3
00:36:47.171 --> 00:36:48.700
one invoice model to rule them
all.

bda32352-a5ee-4f54-a17e-dc796256864d/8193-0
00:36:49.690 --> 00:36:51.500
And this is called Bayesian
model averaging.

bda32352-a5ee-4f54-a17e-dc796256864d/8206-0
00:36:53.260 --> 00:36:55.710
OK, but what are the weights of
that weighted sum?

bda32352-a5ee-4f54-a17e-dc796256864d/8214-0
00:36:55.880 --> 00:36:58.050
So we had a posterior PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/8263-0
00:36:58.560 --> 00:37:02.683
What we want is the one invoice
model to rule them all, the one

bda32352-a5ee-4f54-a17e-dc796256864d/8263-1
00:37:02.683 --> 00:37:06.548
that knew the joint distribution
of all the different model

bda32352-a5ee-4f54-a17e-dc796256864d/8263-2
00:37:06.548 --> 00:37:10.542
design you could have done and
then integrated it to get just

bda32352-a5ee-4f54-a17e-dc796256864d/8263-3
00:37:10.542 --> 00:37:12.410
the thing you wanted to know.

bda32352-a5ee-4f54-a17e-dc796256864d/8290-0
00:37:12.940 --> 00:37:16.323
And that integral can be
approximated with a sum which is

bda32352-a5ee-4f54-a17e-dc796256864d/8290-1
00:37:16.323 --> 00:37:20.056
the product of the past of each
of the different posteriors you

bda32352-a5ee-4f54-a17e-dc796256864d/8290-2
00:37:20.056 --> 00:37:20.930
compute, right?

bda32352-a5ee-4f54-a17e-dc796256864d/8319-0
00:37:20.940 --> 00:37:24.716
You compute posteriors for a
bunch of different logo designs,

bda32352-a5ee-4f54-a17e-dc796256864d/8319-1
00:37:24.716 --> 00:37:28.127
and then you sum them up,
weighted by this thing called

bda32352-a5ee-4f54-a17e-dc796256864d/8319-2
00:37:28.127 --> 00:37:28.370
PCM.

bda32352-a5ee-4f54-a17e-dc796256864d/8326-0
00:37:28.380 --> 00:37:29.840
Given D, that's something new.

bda32352-a5ee-4f54-a17e-dc796256864d/8337-0
00:37:29.850 --> 00:37:33.350
We haven't seen that before, but
is it well?

bda32352-a5ee-4f54-a17e-dc796256864d/8375-0
00:37:33.360 --> 00:37:36.502
It looks like a posterior, and
if you apply Bayes theorem you

bda32352-a5ee-4f54-a17e-dc796256864d/8375-1
00:37:36.502 --> 00:37:39.492
can rewrite it as the product of
another profile, which is

bda32352-a5ee-4f54-a17e-dc796256864d/8375-2
00:37:39.492 --> 00:37:42.330
whatever you want it to be and
the marginal likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/8390-0
00:37:42.440 --> 00:37:46.158
The thing that said, how
consistent your data will with

bda32352-a5ee-4f54-a17e-dc796256864d/8390-1
00:37:46.158 --> 00:37:47.220
your model sign.

bda32352-a5ee-4f54-a17e-dc796256864d/8393-0
00:37:48.420 --> 00:37:48.810
Umm.

bda32352-a5ee-4f54-a17e-dc796256864d/8426-0
00:37:49.200 --> 00:37:51.655
However, if you remember what I
said that you don't actually

bda32352-a5ee-4f54-a17e-dc796256864d/8426-1
00:37:51.655 --> 00:37:54.191
usually get to calculate that
it's not generally calculable at

bda32352-a5ee-4f54-a17e-dc796256864d/8426-2
00:37:54.191 --> 00:37:55.800
the terrible multidimensional
integral.

bda32352-a5ee-4f54-a17e-dc796256864d/8491-0
00:37:57.170 --> 00:38:00.341
You might also Remember Me
saying the transitioning is

bda32352-a5ee-4f54-a17e-dc796256864d/8491-1
00:38:00.341 --> 00:38:03.973
really neat, so transitioning is
really neat and Jing and Chen

bda32352-a5ee-4f54-a17e-dc796256864d/8491-2
00:38:03.973 --> 00:38:07.720
are 2000 people have this really
beautiful proof that shows that

bda32352-a5ee-4f54-a17e-dc796256864d/8491-3
00:38:07.720 --> 00:38:10.661
you can basically use the
probabilities of all the

bda32352-a5ee-4f54-a17e-dc796256864d/8491-4
00:38:10.661 --> 00:38:14.004
different samples that you
calculated on all from all the

bda32352-a5ee-4f54-a17e-dc796256864d/8491-5
00:38:14.004 --> 00:38:17.290
different intermediate PDFs and
combine them together to

bda32352-a5ee-4f54-a17e-dc796256864d/8491-6
00:38:17.290 --> 00:38:19.250
estimate the marginal
likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/8538-0
00:38:19.440 --> 00:38:22.478
So it just something that you
get for free as part of the

bda32352-a5ee-4f54-a17e-dc796256864d/8538-1
00:38:22.478 --> 00:38:25.725
transitioning process and it's
really straightforward to just

bda32352-a5ee-4f54-a17e-dc796256864d/8538-2
00:38:25.725 --> 00:38:28.763
plug and chug through their
proof with crossfading to get

bda32352-a5ee-4f54-a17e-dc796256864d/8538-3
00:38:28.763 --> 00:38:31.800
the same or to get an equivalent
answer for class fading.

bda32352-a5ee-4f54-a17e-dc796256864d/8555-0
00:38:31.810 --> 00:38:34.339
So you can just estimate the
marginal likelihood for free as

bda32352-a5ee-4f54-a17e-dc796256864d/8555-1
00:38:34.339 --> 00:38:35.540
part of the sampling process.

bda32352-a5ee-4f54-a17e-dc796256864d/8578-0
00:38:37.250 --> 00:38:39.852
However, Steven Woo, who you
might remember, came and visited

bda32352-a5ee-4f54-a17e-dc796256864d/8578-1
00:38:39.852 --> 00:38:41.320
last month and gave us a
Seminole.

bda32352-a5ee-4f54-a17e-dc796256864d/8595-0
00:38:42.140 --> 00:38:45.403
I found that unfortunately,
while the proof is right, the

bda32352-a5ee-4f54-a17e-dc796256864d/8595-1
00:38:45.403 --> 00:38:46.640
assumptions aren't OK.

bda32352-a5ee-4f54-a17e-dc796256864d/8623-0
00:38:46.710 --> 00:38:50.061
Basically, they assume all the
samples are at equilibrium and

bda32352-a5ee-4f54-a17e-dc796256864d/8623-1
00:38:50.061 --> 00:38:53.033
if you are familiar with MCMC,
there's this issue with

bda32352-a5ee-4f54-a17e-dc796256864d/8623-2
00:38:53.033 --> 00:38:54.330
something called boning.

bda32352-a5ee-4f54-a17e-dc796256864d/8638-0
00:38:54.340 --> 00:38:56.332
We all takes a while, for
example strategy be at

bda32352-a5ee-4f54-a17e-dc796256864d/8638-1
00:38:56.332 --> 00:38:57.470
equilibrium because of that.

bda32352-a5ee-4f54-a17e-dc796256864d/8661-0
00:38:59.270 --> 00:39:03.086
The the actual the numbers you
get about biased and it's weird,

bda32352-a5ee-4f54-a17e-dc796256864d/8661-1
00:39:03.086 --> 00:39:04.040
but Steven said.

bda32352-a5ee-4f54-a17e-dc796256864d/8701-0
00:39:04.050 --> 00:39:07.123
But if you change the way that
you did the sampling to account

bda32352-a5ee-4f54-a17e-dc796256864d/8701-1
00:39:07.123 --> 00:39:10.292
for Borden, then you could take
this proof and you would in fact

bda32352-a5ee-4f54-a17e-dc796256864d/8701-2
00:39:10.292 --> 00:39:12.730
have a good estimate for the
marginal likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/8726-0
00:39:13.720 --> 00:39:16.780
And it turns out all the things
you need to do were things that

bda32352-a5ee-4f54-a17e-dc796256864d/8726-1
00:39:16.780 --> 00:39:19.170
we already did when we built
catnip from TMC, MC.

bda32352-a5ee-4f54-a17e-dc796256864d/8752-0
00:39:19.180 --> 00:39:22.285
So in theory, we should just be
good like we should be able to

bda32352-a5ee-4f54-a17e-dc796256864d/8752-1
00:39:22.285 --> 00:39:24.848
just run catnip and get an
estimate of the marginal

bda32352-a5ee-4f54-a17e-dc796256864d/8752-2
00:39:24.848 --> 00:39:25.390
likelihood.

bda32352-a5ee-4f54-a17e-dc796256864d/8764-0
00:39:25.400 --> 00:39:26.950
So let's see if that's true.

bda32352-a5ee-4f54-a17e-dc796256864d/8805-0
00:39:26.960 --> 00:39:30.481
Let's run cap for a problem that
has a known analytical solution

bda32352-a5ee-4f54-a17e-dc796256864d/8805-1
00:39:30.481 --> 00:39:33.894
and we can just see whether the
estimate we get from Count MIP

bda32352-a5ee-4f54-a17e-dc796256864d/8805-2
00:39:33.894 --> 00:39:36.710
compare as well with the known
analytical solution.

bda32352-a5ee-4f54-a17e-dc796256864d/8817-0
00:39:37.120 --> 00:39:40.190
Analytical solutions in red
estimate from camp is in black.

bda32352-a5ee-4f54-a17e-dc796256864d/8822-0
00:39:40.340 --> 00:39:41.260
Yeah, I think we're fine.

bda32352-a5ee-4f54-a17e-dc796256864d/8831-0
00:39:43.380 --> 00:39:44.190
Let's give this a try.

bda32352-a5ee-4f54-a17e-dc796256864d/8841-0
00:39:44.200 --> 00:39:47.160
Then let's try Bayesian model
averaging.

bda32352-a5ee-4f54-a17e-dc796256864d/8858-0
00:39:47.170 --> 00:39:50.113
The one model to rule them all,
and so I'm gonna follow an

bda32352-a5ee-4f54-a17e-dc796256864d/8858-1
00:39:50.113 --> 00:39:51.010
example from Zach.

bda32352-a5ee-4f54-a17e-dc796256864d/8864-0
00:39:51.020 --> 00:39:52.670
Do Patel's 2014 people.

bda32352-a5ee-4f54-a17e-dc796256864d/8899-0
00:39:52.860 --> 00:39:55.788
We're going to look at avoid
across strike, slip infinitely

bda32352-a5ee-4f54-a17e-dc796256864d/8899-1
00:39:55.788 --> 00:39:58.912
long strike, slip fault with an
array of gene associations that

bda32352-a5ee-4f54-a17e-dc796256864d/8899-2
00:39:58.912 --> 00:40:00.180
cross the perpendicularly.

bda32352-a5ee-4f54-a17e-dc796256864d/8932-0
00:40:01.060 --> 00:40:04.218
I'm going to solve for slip as a
function of depth, but we don't

bda32352-a5ee-4f54-a17e-dc796256864d/8932-1
00:40:04.218 --> 00:40:07.133
know the elastic structure and
maybe the phone isn't really

bda32352-a5ee-4f54-a17e-dc796256864d/8932-2
00:40:07.133 --> 00:40:07.570
vertical.

bda32352-a5ee-4f54-a17e-dc796256864d/8953-0
00:40:07.860 --> 00:40:10.232
So can we still include the
fault slip even though we don't

bda32352-a5ee-4f54-a17e-dc796256864d/8953-1
00:40:10.232 --> 00:40:11.220
know any of these things?

bda32352-a5ee-4f54-a17e-dc796256864d/8965-0
00:40:12.580 --> 00:40:16.900
I'm so I'm going to take six
different model designs.

bda32352-a5ee-4f54-a17e-dc796256864d/8975-0
00:40:17.900 --> 00:40:19.360
I don't know if any of them are
right.

bda32352-a5ee-4f54-a17e-dc796256864d/8984-0
00:40:19.370 --> 00:40:20.600
I'm going to look at 1/2 space.

bda32352-a5ee-4f54-a17e-dc796256864d/9008-0
00:40:20.820 --> 00:40:23.673
I'm gonna look at the layout
elastic structure, but I don't

bda32352-a5ee-4f54-a17e-dc796256864d/9008-1
00:40:23.673 --> 00:40:25.670
know what the elastic constant
should be.

bda32352-a5ee-4f54-a17e-dc796256864d/9016-0
00:40:25.680 --> 00:40:28.630
So just pick three different
elastic contrasts.

bda32352-a5ee-4f54-a17e-dc796256864d/9026-0
00:40:29.790 --> 00:40:31.720
Maybe there's a compliant zone
around the fault.

bda32352-a5ee-4f54-a17e-dc796256864d/9030-0
00:40:31.730 --> 00:40:32.470
Let's try that.

bda32352-a5ee-4f54-a17e-dc796256864d/9042-0
00:40:32.680 --> 00:40:34.060
Hey, maybe the faults not
different.

bda32352-a5ee-4f54-a17e-dc796256864d/9044-0
00:40:34.070 --> 00:40:34.940
Not protocol.

bda32352-a5ee-4f54-a17e-dc796256864d/9094-0
00:40:35.040 --> 00:40:39.307
Try dipping fault and for these
six different model designs I

bda32352-a5ee-4f54-a17e-dc796256864d/9094-1
00:40:39.307 --> 00:40:43.712
will do this in version which is
now really cheap to do because

bda32352-a5ee-4f54-a17e-dc796256864d/9094-2
00:40:43.712 --> 00:40:47.979
we're using crossfading and red
is the input model that we're

bda32352-a5ee-4f54-a17e-dc796256864d/9094-3
00:40:47.979 --> 00:40:49.080
trying to cover.

bda32352-a5ee-4f54-a17e-dc796256864d/9104-0
00:40:49.490 --> 00:40:51.640
Black is what we inform after
sampling.

bda32352-a5ee-4f54-a17e-dc796256864d/9125-0
00:40:51.650 --> 00:40:55.649
It's the mean of the posterior
samples, and just for reference,

bda32352-a5ee-4f54-a17e-dc796256864d/9125-1
00:40:55.649 --> 00:40:57.960
blue is where the sample or
started.

bda32352-a5ee-4f54-a17e-dc796256864d/9136-0
00:40:58.010 --> 00:41:02.390
It's the conjugate posterior
text difference.

bda32352-a5ee-4f54-a17e-dc796256864d/9160-0
00:41:02.400 --> 00:41:05.700
Smaller designs gives you six
different answers for slip on

bda32352-a5ee-4f54-a17e-dc796256864d/9160-1
00:41:05.700 --> 00:41:09.110
the fault, and there's no way to
know which is quote unquote,

bda32352-a5ee-4f54-a17e-dc796256864d/9160-2
00:41:09.110 --> 00:41:09.440
right?

bda32352-a5ee-4f54-a17e-dc796256864d/9168-0
00:41:10.030 --> 00:41:11.800
Because they offered the data
right?

bda32352-a5ee-4f54-a17e-dc796256864d/9182-0
00:41:12.130 --> 00:41:14.030
They all do a great job getting
the data.

bda32352-a5ee-4f54-a17e-dc796256864d/9194-0
00:41:14.040 --> 00:41:16.320
That's what under determined
invoice problems are like.

bda32352-a5ee-4f54-a17e-dc796256864d/9233-0
00:41:16.790 --> 00:41:20.575
But what we can do is we can use
the fact that we did cross

bda32352-a5ee-4f54-a17e-dc796256864d/9233-1
00:41:20.575 --> 00:41:24.359
fading or transitioning to
estimate the marginal likelihood

bda32352-a5ee-4f54-a17e-dc796256864d/9233-2
00:41:24.359 --> 00:41:28.144
and thus get the posterior
probability associated with each

bda32352-a5ee-4f54-a17e-dc796256864d/9233-3
00:41:28.144 --> 00:41:28.900
model class.

bda32352-a5ee-4f54-a17e-dc796256864d/9317-0
00:41:29.010 --> 00:41:32.328
And that's what's shown in
purple here and then we can use

bda32352-a5ee-4f54-a17e-dc796256864d/9317-1
00:41:32.328 --> 00:41:35.646
these posterior probabilities as
rates to add up these six

bda32352-a5ee-4f54-a17e-dc796256864d/9317-2
00:41:35.646 --> 00:41:39.132
different solutions to make the
Bayesian model average, which

bda32352-a5ee-4f54-a17e-dc796256864d/9317-3
00:41:39.132 --> 00:41:42.225
looks like that, and the
Bayesian model average does a

bda32352-a5ee-4f54-a17e-dc796256864d/9317-4
00:41:42.225 --> 00:41:45.487
really nice job recovering
inputs slip model, despite the

bda32352-a5ee-4f54-a17e-dc796256864d/9317-5
00:41:45.487 --> 00:41:49.142
fact that we used six different
models, all of which were wrong,

bda32352-a5ee-4f54-a17e-dc796256864d/9317-6
00:41:49.142 --> 00:41:52.403
to try and figure out what the
step was, and they want to

bda32352-a5ee-4f54-a17e-dc796256864d/9317-7
00:41:52.403 --> 00:41:53.190
estimate that.

bda32352-a5ee-4f54-a17e-dc796256864d/9327-0
00:41:53.200 --> 00:41:55.306
You'll probably wondering which
of these model designs was

bda32352-a5ee-4f54-a17e-dc796256864d/9327-1
00:41:55.306 --> 00:41:55.520
right?

bda32352-a5ee-4f54-a17e-dc796256864d/9331-0
00:41:55.890 --> 00:41:56.660
None of them.

bda32352-a5ee-4f54-a17e-dc796256864d/9353-0
00:41:56.890 --> 00:42:00.860
None of these are the model
design that I use to generate

bda32352-a5ee-4f54-a17e-dc796256864d/9353-1
00:42:00.860 --> 00:42:02.160
the synthetic data.

bda32352-a5ee-4f54-a17e-dc796256864d/9367-0
00:42:02.370 --> 00:42:04.900
If you're really curious, it was
a later lastic structure.

bda32352-a5ee-4f54-a17e-dc796256864d/9411-0
00:42:04.910 --> 00:42:07.977
There was kind of in between
B&C, but the point is that

bda32352-a5ee-4f54-a17e-dc796256864d/9411-1
00:42:07.977 --> 00:42:11.145
you can recover all the inputs
of model despite the fact that

bda32352-a5ee-4f54-a17e-dc796256864d/9411-2
00:42:11.145 --> 00:42:14.365
you do not know what the model
design should have been and all

bda32352-a5ee-4f54-a17e-dc796256864d/9411-3
00:42:14.365 --> 00:42:16.000
of your model designs are wrong.

bda32352-a5ee-4f54-a17e-dc796256864d/9420-0
00:42:17.290 --> 00:42:20.170
Umm so basic model average.

bda32352-a5ee-4f54-a17e-dc796256864d/9439-0
00:42:20.180 --> 00:42:22.739
It has some pros that you can
mix and match whatever model

bda32352-a5ee-4f54-a17e-dc796256864d/9439-1
00:42:22.739 --> 00:42:24.300
design you're interested in,
right?

bda32352-a5ee-4f54-a17e-dc796256864d/9467-0
00:42:24.310 --> 00:42:27.270
You're not assuming an arrow
structural or you're not looking

bda32352-a5ee-4f54-a17e-dc796256864d/9467-1
00:42:27.270 --> 00:42:29.990
at variations or punctuations
about a particular elastic

bda32352-a5ee-4f54-a17e-dc796256864d/9467-2
00:42:29.990 --> 00:42:31.040
structure or geometry.

bda32352-a5ee-4f54-a17e-dc796256864d/9550-0
00:42:31.050 --> 00:42:33.645
So you can combine things
whatever you want, take into

bda32352-a5ee-4f54-a17e-dc796256864d/9550-1
00:42:33.645 --> 00:42:36.145
compliance zone, take out a
compliance zone, go with

bda32352-a5ee-4f54-a17e-dc796256864d/9550-2
00:42:36.145 --> 00:42:38.833
horizontal layouts, go with
vertical layouts like change

bda32352-a5ee-4f54-a17e-dc796256864d/9550-3
00:42:38.833 --> 00:42:41.664
whatever you want and you can
get all the different results

bda32352-a5ee-4f54-a17e-dc796256864d/9550-4
00:42:41.664 --> 00:42:44.588
for all the different models to
see how they vary rather than

bda32352-a5ee-4f54-a17e-dc796256864d/9550-5
00:42:44.588 --> 00:42:47.654
just having everything buried in
one giant black box and portion

bda32352-a5ee-4f54-a17e-dc796256864d/9550-6
00:42:47.654 --> 00:42:50.531
but the contents that billion
Bayesian model averaging has a

bda32352-a5ee-4f54-a17e-dc796256864d/9550-7
00:42:50.531 --> 00:42:51.380
shrinkage problem.

bda32352-a5ee-4f54-a17e-dc796256864d/9563-0
00:42:51.390 --> 00:42:53.540
It doesn't actually tend to give
you nice way toy.

bda32352-a5ee-4f54-a17e-dc796256864d/9569-0
00:42:53.720 --> 00:42:54.230
Different model.

bda32352-a5ee-4f54-a17e-dc796256864d/9584-0
00:42:54.240 --> 00:42:56.930
Is it tends to go crazy and be
like that's it.

bda32352-a5ee-4f54-a17e-dc796256864d/9599-0
00:42:56.980 --> 00:42:59.386
All my money on that model
class, that's the one that I

bda32352-a5ee-4f54-a17e-dc796256864d/9599-1
00:42:59.386 --> 00:42:59.600
like.

bda32352-a5ee-4f54-a17e-dc796256864d/9614-0
00:43:01.490 --> 00:43:03.840
It also has a problem that it's
really sensitive to your choice

bda32352-a5ee-4f54-a17e-dc796256864d/9614-1
00:43:03.840 --> 00:43:04.170
of prior.

bda32352-a5ee-4f54-a17e-dc796256864d/9629-0
00:43:04.180 --> 00:43:07.920
Also, Jim Back has a people in
2010 where he.

bda32352-a5ee-4f54-a17e-dc796256864d/9638-0
00:43:08.700 --> 00:43:11.970
I wrote well.

bda32352-a5ee-4f54-a17e-dc796256864d/9666-0
00:43:11.980 --> 00:43:15.240
He showed that the marginal
likelihood in log space can be

bda32352-a5ee-4f54-a17e-dc796256864d/9666-1
00:43:15.240 --> 00:43:18.610
described as something that
increases with your data fit and

bda32352-a5ee-4f54-a17e-dc796256864d/9666-2
00:43:18.610 --> 00:43:19.770
is penalized by high.

bda32352-a5ee-4f54-a17e-dc796256864d/9678-0
00:43:19.780 --> 00:43:22.250
How different your posterior is
from your trial?

bda32352-a5ee-4f54-a17e-dc796256864d/9705-0
00:43:22.420 --> 00:43:24.801
That is how much you had to
basically violate your prior in

bda32352-a5ee-4f54-a17e-dc796256864d/9705-1
00:43:24.801 --> 00:43:27.142
order to fit the data, which
means that it's actually very

bda32352-a5ee-4f54-a17e-dc796256864d/9705-2
00:43:27.142 --> 00:43:28.530
sensitive to your choice of
trial.

bda32352-a5ee-4f54-a17e-dc796256864d/9724-0
00:43:28.920 --> 00:43:31.557
So basic model averaging is
elegant in theory, but it can be

bda32352-a5ee-4f54-a17e-dc796256864d/9724-1
00:43:31.557 --> 00:43:32.680
quite fragile in practice.

bda32352-a5ee-4f54-a17e-dc796256864d/9777-0
00:43:34.040 --> 00:43:36.905
Umm, I also want to say that
despite the fact that I freaked

bda32352-a5ee-4f54-a17e-dc796256864d/9777-1
00:43:36.905 --> 00:43:39.864
out with math over the fact that
there was no forward model in

bda32352-a5ee-4f54-a17e-dc796256864d/9777-2
00:43:39.864 --> 00:43:42.494
Crossfading, so I didn't know
what to do with the model

bda32352-a5ee-4f54-a17e-dc796256864d/9777-3
00:43:42.494 --> 00:43:45.312
prediction error, I think you
can actually use a lot of the

bda32352-a5ee-4f54-a17e-dc796256864d/9777-4
00:43:45.312 --> 00:43:46.110
existing methods.

bda32352-a5ee-4f54-a17e-dc796256864d/9805-0
00:43:46.240 --> 00:43:50.015
I mean the reason that they get
updated in a lot of cases is

bda32352-a5ee-4f54-a17e-dc796256864d/9805-1
00:43:50.015 --> 00:43:53.356
because you need a good slip
model in order to do the

bda32352-a5ee-4f54-a17e-dc796256864d/9805-2
00:43:53.356 --> 00:43:54.160
calculations.

bda32352-a5ee-4f54-a17e-dc796256864d/9811-0
00:43:54.170 --> 00:43:54.600
That's the story.

bda32352-a5ee-4f54-a17e-dc796256864d/9847-0
00:43:54.610 --> 00:43:58.251
So, for example, in Zach
Dupattas 2014 people right, you

bda32352-a5ee-4f54-a17e-dc796256864d/9847-1
00:43:58.251 --> 00:44:01.316
need a good slip model to
propagate through the

bda32352-a5ee-4f54-a17e-dc796256864d/9847-2
00:44:01.316 --> 00:44:04.190
perturbations, but you do have a
good model.

bda32352-a5ee-4f54-a17e-dc796256864d/9852-0
00:44:04.200 --> 00:44:05.410
You have the conjugate
posterior.

bda32352-a5ee-4f54-a17e-dc796256864d/9859-0
00:44:05.420 --> 00:44:06.490
That's a good enough model.

bda32352-a5ee-4f54-a17e-dc796256864d/9884-0
00:44:06.500 --> 00:44:10.803
And so just as an example of
that, you know I I calculated a

bda32352-a5ee-4f54-a17e-dc796256864d/9884-1
00:44:10.803 --> 00:44:14.470
conjugate posterior based on a
very dumb AOL model.

bda32352-a5ee-4f54-a17e-dc796256864d/9902-0
00:44:14.580 --> 00:44:18.275
I use that with Zach's
perturbation theory to get a

bda32352-a5ee-4f54-a17e-dc796256864d/9902-1
00:44:18.275 --> 00:44:21.330
nice uh model prediction
covariance model.

bda32352-a5ee-4f54-a17e-dc796256864d/9912-0
00:44:21.520 --> 00:44:23.550
I then calculated a new
conjugate posterior.

bda32352-a5ee-4f54-a17e-dc796256864d/9935-0
00:44:23.820 --> 00:44:28.477
I ran the sampling and it did a
very nice job of recovering the

bda32352-a5ee-4f54-a17e-dc796256864d/9935-1
00:44:28.477 --> 00:44:30.660
true fault model shown in red.

bda32352-a5ee-4f54-a17e-dc796256864d/9950-0
00:44:32.510 --> 00:44:34.232
By the way, did anyone else
notice the real thing that just

bda32352-a5ee-4f54-a17e-dc796256864d/9950-1
00:44:34.232 --> 00:44:34.490
happened?

bda32352-a5ee-4f54-a17e-dc796256864d/9963-0
00:44:34.940 --> 00:44:38.770
Umm, so the red is what we're
trying to recover.

bda32352-a5ee-4f54-a17e-dc796256864d/9975-0
00:44:39.200 --> 00:44:41.870
The black is what you get from
the good inversion.

bda32352-a5ee-4f54-a17e-dc796256864d/9996-0
00:44:41.880 --> 00:44:43.925
You know, the one that has the
backup complaints and strange,

bda32352-a5ee-4f54-a17e-dc796256864d/9996-1
00:44:43.925 --> 00:44:44.980
so it doesn't do anything crazy.

bda32352-a5ee-4f54-a17e-dc796256864d/10012-0
00:44:46.590 --> 00:44:50.565
The blue was the completely
unconstrained analytical

bda32352-a5ee-4f54-a17e-dc796256864d/10012-1
00:44:50.565 --> 00:44:52.740
solution, and it looks great.

bda32352-a5ee-4f54-a17e-dc796256864d/10034-0
00:44:52.890 --> 00:44:56.072
It looks just like the input
model, which suggests that maybe

bda32352-a5ee-4f54-a17e-dc796256864d/10034-1
00:44:56.072 --> 00:44:58.740
you don't need sampling or fancy
inversions at all.

bda32352-a5ee-4f54-a17e-dc796256864d/10064-0
00:44:58.750 --> 00:45:03.159
Maybe completely unconstrained
analytical solutions are fine as

bda32352-a5ee-4f54-a17e-dc796256864d/10064-1
00:45:03.159 --> 00:45:07.360
long as you have a really good
model prediction arrow model.

bda32352-a5ee-4f54-a17e-dc796256864d/10064-2
00:45:07.360 --> 00:45:07.980
You know.

bda32352-a5ee-4f54-a17e-dc796256864d/10096-0
00:45:07.990 --> 00:45:11.303
Basically, maybe the fact that
we do inversions and get back

bda32352-a5ee-4f54-a17e-dc796256864d/10096-1
00:45:11.303 --> 00:45:14.724
models as well falsifying the
wrong direction isn't telling us

bda32352-a5ee-4f54-a17e-dc796256864d/10096-2
00:45:14.724 --> 00:45:15.810
how bad our data is.

bda32352-a5ee-4f54-a17e-dc796256864d/10106-0
00:45:15.820 --> 00:45:17.360
It can training step on the
foot.

bda32352-a5ee-4f54-a17e-dc796256864d/10154-0
00:45:17.370 --> 00:45:20.739
Maybe it's really telling us how
lousy our model design is, and

bda32352-a5ee-4f54-a17e-dc796256864d/10154-1
00:45:20.739 --> 00:45:24.213
how pull structure is, and if we
just made a better ill structure

bda32352-a5ee-4f54-a17e-dc796256864d/10154-2
00:45:24.213 --> 00:45:27.266
that better understood the
effects of arrows in our model

bda32352-a5ee-4f54-a17e-dc796256864d/10154-3
00:45:27.266 --> 00:45:30.740
design, we wouldn't even have to
worry about the invasion at all.

bda32352-a5ee-4f54-a17e-dc796256864d/10160-0
00:45:32.140 --> 00:45:34.140
OK conclusions.

bda32352-a5ee-4f54-a17e-dc796256864d/10166-0
00:45:35.260 --> 00:45:36.730
We developed crossfade sampling.

bda32352-a5ee-4f54-a17e-dc796256864d/10180-0
00:45:36.740 --> 00:45:39.702
It's a very efficient method for
simulating Bayesian posterior

bda32352-a5ee-4f54-a17e-dc796256864d/10180-1
00:45:39.702 --> 00:45:39.890
PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/10193-0
00:45:40.240 --> 00:45:43.250
That is, it requires very few
samples to simulate the

bda32352-a5ee-4f54-a17e-dc796256864d/10193-1
00:45:43.250 --> 00:45:44.030
posterior PDF.

bda32352-a5ee-4f54-a17e-dc796256864d/10221-0
00:45:44.160 --> 00:45:46.984
It also has zero computational
cost for big data because you

bda32352-a5ee-4f54-a17e-dc796256864d/10221-1
00:45:46.984 --> 00:45:49.760
never evaluate the forward model
or the misfit to the data.

bda32352-a5ee-4f54-a17e-dc796256864d/10240-0
00:45:50.520 --> 00:45:53.088
Fitting a model to date without
having the the forward model or

bda32352-a5ee-4f54-a17e-dc796256864d/10240-1
00:45:53.088 --> 00:45:53.730
the data misfit.

bda32352-a5ee-4f54-a17e-dc796256864d/10242-0
00:45:53.980 --> 00:45:54.690
It could be big.

bda32352-a5ee-4f54-a17e-dc796256864d/10278-0
00:45:57.050 --> 00:45:59.523
However, like CrossFit, sampling
is not applicable to all

bda32352-a5ee-4f54-a17e-dc796256864d/10278-1
00:45:59.523 --> 00:46:02.165
problems, but it is applicable
to a large family of problems,

bda32352-a5ee-4f54-a17e-dc796256864d/10278-2
00:46:02.165 --> 00:46:04.680
and I know I keep talking about
earthquake rupture models.

bda32352-a5ee-4f54-a17e-dc796256864d/10309-0
00:46:05.710 --> 00:46:08.396
I'm sorry I can't help it, but
actually you know there's

bda32352-a5ee-4f54-a17e-dc796256864d/10309-1
00:46:08.396 --> 00:46:11.412
nothing about this methodology
that is specific to fault models

bda32352-a5ee-4f54-a17e-dc796256864d/10309-2
00:46:11.412 --> 00:46:13.390
or linear problems or anything
like that.

bda32352-a5ee-4f54-a17e-dc796256864d/10332-0
00:46:13.400 --> 00:46:16.569
It just requires that there
exist for your likelihood some

bda32352-a5ee-4f54-a17e-dc796256864d/10332-1
00:46:16.569 --> 00:46:19.200
other posterior that can be
directly stimulated.

bda32352-a5ee-4f54-a17e-dc796256864d/10338-0
00:46:19.330 --> 00:46:21.190
Was basically means look for
conjugate files.

bda32352-a5ee-4f54-a17e-dc796256864d/10359-0
00:46:22.610 --> 00:46:25.474
Umm I wanna stress the
accounting for model prediction

bda32352-a5ee-4f54-a17e-dc796256864d/10359-1
00:46:25.474 --> 00:46:26.880
errors is really important.

bda32352-a5ee-4f54-a17e-dc796256864d/10398-0
00:46:27.310 --> 00:46:30.452
All models are wrong and if you
don't account for the prediction

bda32352-a5ee-4f54-a17e-dc796256864d/10398-1
00:46:30.452 --> 00:46:33.304
error, they're not even useful
and and also maybe we don't

bda32352-a5ee-4f54-a17e-dc796256864d/10398-2
00:46:33.304 --> 00:46:36.059
actually need fancy non
analytical inversions with fancy

bda32352-a5ee-4f54-a17e-dc796256864d/10398-3
00:46:36.059 --> 00:46:36.590
constrains.

bda32352-a5ee-4f54-a17e-dc796256864d/10408-0
00:46:36.600 --> 00:46:39.400
Maybe we just need better
prediction error models?

bda32352-a5ee-4f54-a17e-dc796256864d/10479-0
00:46:39.410 --> 00:46:42.775
I don't know, but that wasn't
really real outcome and despite

bda32352-a5ee-4f54-a17e-dc796256864d/10479-1
00:46:42.775 --> 00:46:46.302
the fact that crossword sampling
does not have model predictions

bda32352-a5ee-4f54-a17e-dc796256864d/10479-2
00:46:46.302 --> 00:46:49.829
because no forward model and no
data misfit, you can still use a

bda32352-a5ee-4f54-a17e-dc796256864d/10479-3
00:46:49.829 --> 00:46:52.488
lot of the existing
methodologies for estimating

bda32352-a5ee-4f54-a17e-dc796256864d/10479-4
00:46:52.488 --> 00:46:55.853
model prediction errors, because
the conjugate posterior is a

bda32352-a5ee-4f54-a17e-dc796256864d/10479-5
00:46:55.853 --> 00:46:58.620
good enough model to use to get
that started. Umm.

bda32352-a5ee-4f54-a17e-dc796256864d/10496-0
00:46:58.630 --> 00:47:01.361
But also because CrossFit
sampling bet you calculate the

bda32352-a5ee-4f54-a17e-dc796256864d/10496-1
00:47:01.361 --> 00:47:02.750
marginal likelihood for free.

bda32352-a5ee-4f54-a17e-dc796256864d/10510-0
00:47:03.020 --> 00:47:05.300
You could also try, you know,
Bayesian model averaging.

bda32352-a5ee-4f54-a17e-dc796256864d/10517-0
00:47:05.310 --> 00:47:06.900
The one invoice model to rule
them all.

bda32352-a5ee-4f54-a17e-dc796256864d/10519-0
00:47:07.980 --> 00:47:08.430
Umm.

bda32352-a5ee-4f54-a17e-dc796256864d/10532-0
00:47:08.480 --> 00:47:12.190
And so finally, President of
future work and more friendship.

bda32352-a5ee-4f54-a17e-dc796256864d/10553-0
00:47:12.260 --> 00:47:16.080
I think what we've done is we've
really just moved the goal post

bda32352-a5ee-4f54-a17e-dc796256864d/10553-1
00:47:16.080 --> 00:47:18.430
for Bayesian North Creek models,
right?

bda32352-a5ee-4f54-a17e-dc796256864d/10602-0
00:47:18.440 --> 00:47:21.682
So when this talk started, which
probably feels like it was many

bda32352-a5ee-4f54-a17e-dc796256864d/10602-1
00:47:21.682 --> 00:47:24.774
years ago at this point, like
doing a normal earthquake fault

bda32352-a5ee-4f54-a17e-dc796256864d/10602-2
00:47:24.774 --> 00:47:27.367
model was a super computer
problem and doing like a

bda32352-a5ee-4f54-a17e-dc796256864d/10602-3
00:47:27.367 --> 00:47:30.110
submeter resolution earthquake
model wasn't happening.

bda32352-a5ee-4f54-a17e-dc796256864d/10644-0
00:47:30.640 --> 00:47:33.323
But now we've moved the
goalpost, so the doing sort of a

bda32352-a5ee-4f54-a17e-dc796256864d/10644-1
00:47:33.323 --> 00:47:35.958
normal earthquake Ford model,
like my friend Jess, says

bda32352-a5ee-4f54-a17e-dc796256864d/10644-2
00:47:35.958 --> 00:47:37.840
Richcrest model should be fun
and easy.

bda32352-a5ee-4f54-a17e-dc796256864d/10665-0
00:47:38.220 --> 00:47:40.608
Like everything I showed today,
I ran on my work station in

bda32352-a5ee-4f54-a17e-dc796256864d/10665-1
00:47:40.608 --> 00:47:41.960
MATLAB and almost no time at
all.

bda32352-a5ee-4f54-a17e-dc796256864d/10718-0
00:47:42.210 --> 00:47:45.304
That should be the sort of the
scale of doing regular

bda32352-a5ee-4f54-a17e-dc796256864d/10718-1
00:47:45.304 --> 00:47:48.912
earthquake models now, but of
course, doing something like Ben

bda32352-a5ee-4f54-a17e-dc796256864d/10718-2
00:47:48.912 --> 00:47:52.120
and Josie's sub meet US
resolution 10 million light our

bda32352-a5ee-4f54-a17e-dc796256864d/10718-3
00:47:52.120 --> 00:47:55.900
data point thing that's now, now
that's a super computer problem.

bda32352-a5ee-4f54-a17e-dc796256864d/10734-0
00:47:55.910 --> 00:47:57.907
At least it's doable, but
they're still gonna be super

bda32352-a5ee-4f54-a17e-dc796256864d/10734-1
00:47:57.907 --> 00:47:58.560
computer for that.

bda32352-a5ee-4f54-a17e-dc796256864d/10779-0
00:47:58.670 --> 00:48:01.822
So I'll over the last year, I
have worked with about Josh and

bda32352-a5ee-4f54-a17e-dc796256864d/10779-1
00:48:01.822 --> 00:48:05.075
Chris Hensley and NASA Ames and
we have implemented across face

bda32352-a5ee-4f54-a17e-dc796256864d/10779-2
00:48:05.075 --> 00:48:07.769
sampling on the NASA bleeding
supercomputer with GPU

bda32352-a5ee-4f54-a17e-dc796256864d/10779-3
00:48:07.769 --> 00:48:09.700
acceleration and it's very
efficient.

bda32352-a5ee-4f54-a17e-dc796256864d/10795-0
00:48:09.710 --> 00:48:12.850
So next stop, that's model that
South and app earthquake.

bda32352-a5ee-4f54-a17e-dc796256864d/10797-0
00:48:14.120 --> 00:48:14.440
Thank you.

bda32352-a5ee-4f54-a17e-dc796256864d/10809-0
00:48:23.000 --> 00:48:24.910
Thanks Sarah for a fantastic
talk.

bda32352-a5ee-4f54-a17e-dc796256864d/10823-0
00:48:24.960 --> 00:48:27.260
Uh, let's open it up to
questions.

bda32352-a5ee-4f54-a17e-dc796256864d/10828-0
00:48:27.310 --> 00:48:30.080
Strains in the room online.

bda32352-a5ee-4f54-a17e-dc796256864d/10830-0
00:48:34.740 --> 00:48:35.100
Ben.

bda32352-a5ee-4f54-a17e-dc796256864d/10835-0
00:48:38.470 --> 00:48:39.070
Coming up.

bda32352-a5ee-4f54-a17e-dc796256864d/10840-0
00:48:40.330 --> 00:48:41.020
Hey, Sarah.

bda32352-a5ee-4f54-a17e-dc796256864d/10842-0
00:48:41.030 --> 00:48:41.560
Thanks.

bda32352-a5ee-4f54-a17e-dc796256864d/10846-0
00:48:41.950 --> 00:48:42.520
Thanks so much.

bda32352-a5ee-4f54-a17e-dc796256864d/10881-0
00:48:42.530 --> 00:48:47.838
I I neglected in my introduction
to say that you have no

bda32352-a5ee-4f54-a17e-dc796256864d/10881-1
00:48:47.838 --> 00:48:52.960
financial interest in
conjugatepriors.com just for I'm

bda32352-a5ee-4f54-a17e-dc796256864d/10883-0
00:48:50.930 --> 00:48:52.550
Umm, that's true.

bda32352-a5ee-4f54-a17e-dc796256864d/10876-0
00:48:51.140 --> 00:48:51.520
I don't know.

bda32352-a5ee-4f54-a17e-dc796256864d/10881-2
00:48:52.960 --> 00:48:54.170
the founding.

bda32352-a5ee-4f54-a17e-dc796256864d/10903-0
00:48:54.180 --> 00:48:58.447
I'm the CEO and founder of that,
so I just thought, yeah, umm,

bda32352-a5ee-4f54-a17e-dc796256864d/10917-0
00:48:54.900 --> 00:48:55.110
Here.

bda32352-a5ee-4f54-a17e-dc796256864d/10903-1
00:48:58.447 --> 00:48:58.650
no.

bda32352-a5ee-4f54-a17e-dc796256864d/10915-0
00:48:58.660 --> 00:49:01.700
Could could you go back to the
Bayesian model averaging slide?

bda32352-a5ee-4f54-a17e-dc796256864d/10916-0
00:49:02.710 --> 00:49:02.810
No.

bda32352-a5ee-4f54-a17e-dc796256864d/10932-0
00:49:07.700 --> 00:49:13.290
Yeah, so so have you done the
exercise of?

bda32352-a5ee-4f54-a17e-dc796256864d/10972-0
00:49:13.300 --> 00:49:17.110
So you created the forward model
with something between B&C

bda32352-a5ee-4f54-a17e-dc796256864d/10972-1
00:49:17.110 --> 00:49:20.801
and have you done the exercise
of seeing what the basic model

bda32352-a5ee-4f54-a17e-dc796256864d/10952-0
00:49:17.290 --> 00:49:17.540
Ah.

bda32352-a5ee-4f54-a17e-dc796256864d/10972-2
00:49:20.801 --> 00:49:22.170
average would give you?

bda32352-a5ee-4f54-a17e-dc796256864d/10976-0
00:49:22.180 --> 00:49:24.340
Without B&C as model
classes.

bda32352-a5ee-4f54-a17e-dc796256864d/10988-0
00:49:27.310 --> 00:49:29.880
Yeah, kind of fragile because
it.

bda32352-a5ee-4f54-a17e-dc796256864d/10994-0
00:49:28.940 --> 00:49:29.430
Little worse.

bda32352-a5ee-4f54-a17e-dc796256864d/10990-0
00:49:29.930 --> 00:49:30.660
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/10996-0
00:49:30.670 --> 00:49:31.450
No, no, it's not that.

bda32352-a5ee-4f54-a17e-dc796256864d/11018-0
00:49:31.510 --> 00:49:36.840
It's not that it's was, it's
that you know the I the

bda32352-a5ee-4f54-a17e-dc796256864d/11018-1
00:49:36.840 --> 00:49:38.750
probability, right?

bda32352-a5ee-4f54-a17e-dc796256864d/11025-0
00:49:38.760 --> 00:49:39.880
So these are down by zero.

bda32352-a5ee-4f54-a17e-dc796256864d/11038-0
00:49:39.890 --> 00:49:42.420
So these these all go away and
all these things come up.

bda32352-a5ee-4f54-a17e-dc796256864d/11051-0
00:49:42.430 --> 00:49:44.400
And so then half space comes up
a lot.

bda32352-a5ee-4f54-a17e-dc796256864d/11055-0
00:49:44.410 --> 00:49:45.860
Strong contrast comes up a lot.

bda32352-a5ee-4f54-a17e-dc796256864d/11069-0
00:49:47.820 --> 00:49:50.310
Uh, because wait, cause this
this is the probability.

bda32352-a5ee-4f54-a17e-dc796256864d/11081-0
00:49:50.320 --> 00:49:51.890
So these are normalized to sum
to one.

bda32352-a5ee-4f54-a17e-dc796256864d/11086-0
00:49:52.920 --> 00:49:54.330
So these two disappear.

bda32352-a5ee-4f54-a17e-dc796256864d/11089-0
00:49:54.380 --> 00:49:55.420
All these numbers come up.

bda32352-a5ee-4f54-a17e-dc796256864d/11103-0
00:49:57.240 --> 00:50:02.158
Half space and strong contrast
are now the leading contenders,

bda32352-a5ee-4f54-a17e-dc796256864d/11103-1
00:50:02.158 --> 00:50:02.470
but.

bda32352-a5ee-4f54-a17e-dc796256864d/11130-0
00:50:04.900 --> 00:50:08.100
Whether or not they sum together
well, well, cause like strong

bda32352-a5ee-4f54-a17e-dc796256864d/11130-1
00:50:08.100 --> 00:50:10.030
contrast is kind of terrible is
iffy.

bda32352-a5ee-4f54-a17e-dc796256864d/11148-0
00:50:10.400 --> 00:50:15.060
And also whether it gives them
like relative good relative

bda32352-a5ee-4f54-a17e-dc796256864d/11148-1
00:50:15.060 --> 00:50:16.560
rates between them.

bda32352-a5ee-4f54-a17e-dc796256864d/11155-0
00:50:16.570 --> 00:50:18.140
I remember there's a shrinkage
problem, right?

bda32352-a5ee-4f54-a17e-dc796256864d/11183-0
00:50:18.150 --> 00:50:21.251
It's always in danger of being
like, yeah, maybe we just go

bda32352-a5ee-4f54-a17e-dc796256864d/11183-1
00:50:21.251 --> 00:50:24.300
with half space, so maybe we
just go with strong contrast,

bda32352-a5ee-4f54-a17e-dc796256864d/11183-2
00:50:24.300 --> 00:50:24.610
right?

bda32352-a5ee-4f54-a17e-dc796256864d/11222-0
00:50:26.180 --> 00:50:29.199
A another way of thinking like
is even if I had weak or more

bda32352-a5ee-4f54-a17e-dc796256864d/11222-1
00:50:29.199 --> 00:50:32.069
but not both of them, like if in
a world where I only had

bda32352-a5ee-4f54-a17e-dc796256864d/11222-2
00:50:32.069 --> 00:50:33.800
involved we contrast but not
more.

bda32352-a5ee-4f54-a17e-dc796256864d/11232-0
00:50:33.870 --> 00:50:35.760
We contrast with just one by
your answer.

bda32352-a5ee-4f54-a17e-dc796256864d/11237-0
00:50:35.770 --> 00:50:37.090
Would basically just been weak
contrast.

bda32352-a5ee-4f54-a17e-dc796256864d/11290-0
00:50:39.040 --> 00:50:42.000
But in terms of the in terms of
the final slip distribution, is

bda32352-a5ee-4f54-a17e-dc796256864d/11290-1
00:50:42.000 --> 00:50:44.820
it still, would it still be
pretty good independent of model

bda32352-a5ee-4f54-a17e-dc796256864d/11290-2
00:50:44.820 --> 00:50:47.733
class like we don't care what
the model class is, we just care

bda32352-a5ee-4f54-a17e-dc796256864d/11290-3
00:50:47.733 --> 00:50:49.120
what the slip distribution is.

bda32352-a5ee-4f54-a17e-dc796256864d/11307-0
00:50:51.320 --> 00:50:53.990
Well, it it it depends on
whether or not you fed it.

bda32352-a5ee-4f54-a17e-dc796256864d/11318-0
00:50:54.000 --> 00:50:56.315
Anything that that can get you
something that that's good,

bda32352-a5ee-4f54-a17e-dc796256864d/11318-1
00:50:56.315 --> 00:50:56.550
right?

bda32352-a5ee-4f54-a17e-dc796256864d/11351-0
00:50:56.560 --> 00:51:00.225
So if you if more contrast
wasn't here and you just had

bda32352-a5ee-4f54-a17e-dc796256864d/11351-1
00:51:00.225 --> 00:51:04.085
weak contrast, then basically
the BMA would look like like

bda32352-a5ee-4f54-a17e-dc796256864d/11351-2
00:51:04.085 --> 00:51:07.160
this, right, which is not quite
as good maybe.

bda32352-a5ee-4f54-a17e-dc796256864d/11359-0
00:51:07.170 --> 00:51:08.280
But you know it's not bad.

bda32352-a5ee-4f54-a17e-dc796256864d/11373-0
00:51:08.290 --> 00:51:09.700
But of course we didn't have
weak contest.

bda32352-a5ee-4f54-a17e-dc796256864d/11408-0
00:51:09.710 --> 00:51:12.432
If you only had more contrast
than, you would basically only

bda32352-a5ee-4f54-a17e-dc796256864d/11408-1
00:51:12.432 --> 00:51:15.333
have this answer, which is looks
a little bit worse, but this is

bda32352-a5ee-4f54-a17e-dc796256864d/11403-0
00:51:14.170 --> 00:51:14.640
Right, right.

bda32352-a5ee-4f54-a17e-dc796256864d/11408-2
00:51:15.333 --> 00:51:17.340
what I mean by being kind of
fragile, right?

bda32352-a5ee-4f54-a17e-dc796256864d/11453-0
00:51:17.350 --> 00:51:20.990
It it depends on whether or not
you gave it a field of things

bda32352-a5ee-4f54-a17e-dc796256864d/11453-1
00:51:20.990 --> 00:51:24.631
that were nice for it to pick
from, and also enough more than

bda32352-a5ee-4f54-a17e-dc796256864d/11453-2
00:51:24.631 --> 00:51:28.271
one of them was an OK enough
contender to actually show up in

bda32352-a5ee-4f54-a17e-dc796256864d/11453-3
00:51:28.271 --> 00:51:28.740
the end.

bda32352-a5ee-4f54-a17e-dc796256864d/11479-0
00:51:31.580 --> 00:51:34.328
But the point being that all of
these are analytical solutions,

bda32352-a5ee-4f54-a17e-dc796256864d/11479-1
00:51:34.328 --> 00:51:36.560
so it's something and and you
know the codes exist.

bda32352-a5ee-4f54-a17e-dc796256864d/11530-0
00:51:36.570 --> 00:51:40.201
So it's something that kind of
should should be done generally

bda32352-a5ee-4f54-a17e-dc796256864d/11530-1
00:51:40.201 --> 00:51:43.832
or they're, you know, you the
the it's as you pointed out it's

bda32352-a5ee-4f54-a17e-dc796256864d/11528-0
00:51:42.090 --> 00:51:45.840
It's it's now computationally
easy, so like it's on the table.

bda32352-a5ee-4f54-a17e-dc796256864d/11530-2
00:51:43.832 --> 00:51:45.330
very doable, right, right.

bda32352-a5ee-4f54-a17e-dc796256864d/11542-0
00:51:45.850 --> 00:51:48.000
Now it's it's another tool in
the tool bag.

bda32352-a5ee-4f54-a17e-dc796256864d/11546-0
00:51:48.290 --> 00:51:48.470
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/11548-0
00:51:49.060 --> 00:51:50.250
Do we want to do it?

bda32352-a5ee-4f54-a17e-dc796256864d/11558-0
00:51:50.260 --> 00:51:51.710
I don't know, but it's but it.

bda32352-a5ee-4f54-a17e-dc796256864d/11571-0
00:51:51.720 --> 00:51:54.012
But the at least we can ask that
question now, because now it

bda32352-a5ee-4f54-a17e-dc796256864d/11571-1
00:51:54.012 --> 00:51:54.270
exists.

bda32352-a5ee-4f54-a17e-dc796256864d/11600-0
00:51:58.210 --> 00:52:01.010
Uh, Sue, do you wanna unmute
yourself and ask your question?

bda32352-a5ee-4f54-a17e-dc796256864d/11601-0
00:51:59.640 --> 00:52:01.670
Do you wanna unmute yourself and
ask your question?

bda32352-a5ee-4f54-a17e-dc796256864d/11607-0
00:52:02.620 --> 00:52:03.360
Sure, Sarah.

bda32352-a5ee-4f54-a17e-dc796256864d/11649-0
00:52:03.370 --> 00:52:06.662
That was amazing and I think I
know the answer to this, but for

bda32352-a5ee-4f54-a17e-dc796256864d/11649-1
00:52:06.662 --> 00:52:09.902
those of us who are struggling
to catch up, some of the things

bda32352-a5ee-4f54-a17e-dc796256864d/11649-2
00:52:09.902 --> 00:52:13.039
you say make it sound like the
data don't matter and clearly

bda32352-a5ee-4f54-a17e-dc796256864d/11649-3
00:52:13.039 --> 00:52:13.450
they do.

bda32352-a5ee-4f54-a17e-dc796256864d/11663-0
00:52:13.460 --> 00:52:17.100
So in 100 words or less or 50,
can you summarize?

bda32352-a5ee-4f54-a17e-dc796256864d/11681-0
00:52:18.300 --> 00:52:22.596
How and why the data are used
ohm and why why we're still

bda32352-a5ee-4f54-a17e-dc796256864d/11681-1
00:52:22.596 --> 00:52:23.780
collecting them?

bda32352-a5ee-4f54-a17e-dc796256864d/11716-0
00:52:26.330 --> 00:52:33.270
But well, the data or the only
that we have so right.

bda32352-a5ee-4f54-a17e-dc796256864d/11710-0
00:52:27.850 --> 00:52:32.060
Well, the data, all the only
thing that we have so.

bda32352-a5ee-4f54-a17e-dc796256864d/11727-0
00:52:34.610 --> 00:52:37.500
But exactly, I mean, they're
used in this process.

bda32352-a5ee-4f54-a17e-dc796256864d/11723-0
00:52:35.120 --> 00:52:35.440
I mean.

bda32352-a5ee-4f54-a17e-dc796256864d/11736-0
00:52:37.630 --> 00:52:39.910
Is the part that I was
struggling a little bit with.

bda32352-a5ee-4f54-a17e-dc796256864d/11741-0
00:52:42.040 --> 00:52:42.300
Good.

bda32352-a5ee-4f54-a17e-dc796256864d/11749-0
00:52:43.160 --> 00:52:45.910
So the umm that.

bda32352-a5ee-4f54-a17e-dc796256864d/11747-0
00:52:43.720 --> 00:52:44.440
So the.

bda32352-a5ee-4f54-a17e-dc796256864d/11750-0
00:52:46.290 --> 00:52:46.520
That.

bda32352-a5ee-4f54-a17e-dc796256864d/11762-0
00:53:00.110 --> 00:53:01.220
So it's the same.

bda32352-a5ee-4f54-a17e-dc796256864d/11766-0
00:53:01.270 --> 00:53:03.420
It's the same problem, right?

bda32352-a5ee-4f54-a17e-dc796256864d/11799-0
00:53:03.430 --> 00:53:06.747
It's the same formulation for
getting to a posterior PDF that

bda32352-a5ee-4f54-a17e-dc796256864d/11799-1
00:53:06.747 --> 00:53:09.957
is a product of your the things
that fit your data and your

bda32352-a5ee-4f54-a17e-dc796256864d/11799-2
00:53:09.957 --> 00:53:10.920
prior assumptions.

bda32352-a5ee-4f54-a17e-dc796256864d/11852-0
00:53:11.390 --> 00:53:15.215
The point is that we'll just now
rewriting that exact same PDF as

bda32352-a5ee-4f54-a17e-dc796256864d/11852-1
00:53:15.215 --> 00:53:18.634
the product of an analytical
solution, which means that it

bda32352-a5ee-4f54-a17e-dc796256864d/11852-2
00:53:18.634 --> 00:53:22.227
analytically incorporates all
the information about your data

bda32352-a5ee-4f54-a17e-dc796256864d/11852-3
00:53:22.227 --> 00:53:25.183
and forward model and the
differences between that

bda32352-a5ee-4f54-a17e-dc796256864d/11852-4
00:53:25.183 --> 00:53:28.370
analytical solution and the
thing you actually wanted.

bda32352-a5ee-4f54-a17e-dc796256864d/11899-0
00:53:29.000 --> 00:53:33.042
So before we start this, we use
the data to obtain an analytical

bda32352-a5ee-4f54-a17e-dc796256864d/11858-0
00:53:29.680 --> 00:53:30.080
So.

bda32352-a5ee-4f54-a17e-dc796256864d/11899-1
00:53:33.042 --> 00:53:36.400
answer it and we have an
analytical mapping from data

bda32352-a5ee-4f54-a17e-dc796256864d/11899-2
00:53:36.400 --> 00:53:40.318
space to model space and we are
now in model space and we will

bda32352-a5ee-4f54-a17e-dc796256864d/11899-3
00:53:40.318 --> 00:53:41.810
never leave model space.

bda32352-a5ee-4f54-a17e-dc796256864d/11933-0
00:53:41.820 --> 00:53:43.937
We will do everything we want to
do in terms of model

bda32352-a5ee-4f54-a17e-dc796256864d/11933-1
00:53:43.937 --> 00:53:46.249
constraints, in model space
without having to look back to

bda32352-a5ee-4f54-a17e-dc796256864d/11933-2
00:53:46.249 --> 00:53:48.600
the data because we already took
care of that analytically.

bda32352-a5ee-4f54-a17e-dc796256864d/11936-0
00:53:50.450 --> 00:53:50.840
Great.

bda32352-a5ee-4f54-a17e-dc796256864d/11938-0
00:53:50.850 --> 00:53:51.150
Thank you.

bda32352-a5ee-4f54-a17e-dc796256864d/11945-0
00:53:59.160 --> 00:54:00.290
Andy Michaels got his hand up.

bda32352-a5ee-4f54-a17e-dc796256864d/11966-0
00:54:00.300 --> 00:54:02.840
Do you wanna meet yourself and
ask your question?

bda32352-a5ee-4f54-a17e-dc796256864d/11961-0
00:54:03.520 --> 00:54:04.130
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/11977-0
00:54:04.180 --> 00:54:07.705
Can you go back to the Bayesian
model averaging slide the Emma

bda32352-a5ee-4f54-a17e-dc796256864d/11977-1
00:54:07.705 --> 00:54:08.040
slide?

bda32352-a5ee-4f54-a17e-dc796256864d/11984-0
00:54:10.750 --> 00:54:11.780
So I I have.

bda32352-a5ee-4f54-a17e-dc796256864d/11996-0
00:54:11.790 --> 00:54:15.620
I'm somewhere in the same boat
with Sue struggling to keep up.

bda32352-a5ee-4f54-a17e-dc796256864d/12008-0
00:54:15.630 --> 00:54:18.005
But you you did something here
that that I know something

bda32352-a5ee-4f54-a17e-dc796256864d/12008-1
00:54:18.005 --> 00:54:18.250
about.

bda32352-a5ee-4f54-a17e-dc796256864d/12041-0
00:54:20.560 --> 00:54:23.774
So the the question Ben asked
right where the you take out two

bda32352-a5ee-4f54-a17e-dc796256864d/12041-1
00:54:23.774 --> 00:54:26.630
of the models, the two good ones
and then what happens.

bda32352-a5ee-4f54-a17e-dc796256864d/12074-0
00:54:27.560 --> 00:54:30.382
So there's a lot of work on
ensemble modeling and

bda32352-a5ee-4f54-a17e-dc796256864d/12074-1
00:54:30.382 --> 00:54:33.711
forecasting and generally we
found that the Bayesian model

bda32352-a5ee-4f54-a17e-dc796256864d/12074-2
00:54:33.711 --> 00:54:36.870
average this is starts with the
paper by Warner Masaki.

bda32352-a5ee-4f54-a17e-dc796256864d/12100-0
00:54:36.880 --> 00:54:40.293
So really, Warner found it, and
some of us have have seen the

bda32352-a5ee-4f54-a17e-dc796256864d/12100-1
00:54:40.293 --> 00:54:42.660
same effect in our work paper
with Andrew.

bda32352-a5ee-4f54-a17e-dc796256864d/12135-0
00:54:42.670 --> 00:54:46.999
And I wrote show this found this
too that the Bayesian model

bda32352-a5ee-4f54-a17e-dc796256864d/12135-1
00:54:46.999 --> 00:54:51.185
averaging almost turns into
models selection as opposed to

bda32352-a5ee-4f54-a17e-dc796256864d/12127-0
00:54:50.570 --> 00:54:50.780
Yep.

bda32352-a5ee-4f54-a17e-dc796256864d/12135-2
00:54:51.185 --> 00:54:53.810
model averaging and for
forecasting.

bda32352-a5ee-4f54-a17e-dc796256864d/12138-0
00:54:52.590 --> 00:54:53.720
That's the shrinkage problem.

bda32352-a5ee-4f54-a17e-dc796256864d/12148-0
00:54:54.190 --> 00:54:56.280
Yeah, for forecasting purposes
other.

bda32352-a5ee-4f54-a17e-dc796256864d/12176-0
00:54:57.140 --> 00:55:01.697
UM, yeah, other averaging
choices that Warners looked at

bda32352-a5ee-4f54-a17e-dc796256864d/12176-1
00:55:01.697 --> 00:55:06.572
and that we've tried provide
actually better results because

bda32352-a5ee-4f54-a17e-dc796256864d/12176-2
00:55:06.572 --> 00:55:08.970
they don't tend to just throw.

bda32352-a5ee-4f54-a17e-dc796256864d/12195-0
00:55:08.980 --> 00:55:12.548
I mean, hopefully we're putting
in only things that have some

bda32352-a5ee-4f54-a17e-dc796256864d/12195-1
00:55:12.548 --> 00:55:15.310
reasonable physical basis or
statistical basis.

bda32352-a5ee-4f54-a17e-dc796256864d/12211-0
00:55:15.320 --> 00:55:18.286
And so we don't really want to
just throw them out and have our

bda32352-a5ee-4f54-a17e-dc796256864d/12211-1
00:55:18.286 --> 00:55:18.610
models.

bda32352-a5ee-4f54-a17e-dc796256864d/12233-0
00:55:18.620 --> 00:55:21.265
Like when one likelihood goes up
like also that one becomes the

bda32352-a5ee-4f54-a17e-dc796256864d/12233-1
00:55:21.265 --> 00:55:23.290
model, then later another one
becomes the model.

bda32352-a5ee-4f54-a17e-dc796256864d/12245-0
00:55:23.520 --> 00:55:27.170
So we get sort of a smoother,
more even average.

bda32352-a5ee-4f54-a17e-dc796256864d/12289-0
00:55:27.420 --> 00:55:31.499
So the question is it with all
of the theory that goes in here,

bda32352-a5ee-4f54-a17e-dc796256864d/12289-1
00:55:31.499 --> 00:55:35.196
if you tried putting in some
other averaging algorithm at

bda32352-a5ee-4f54-a17e-dc796256864d/12289-2
00:55:35.196 --> 00:55:39.019
this step, but it just blow up
all the math so that nothing

bda32352-a5ee-4f54-a17e-dc796256864d/12289-3
00:55:39.019 --> 00:55:39.720
then works.

bda32352-a5ee-4f54-a17e-dc796256864d/12304-0
00:55:39.780 --> 00:55:42.560
So could you just try try some
other things?

bda32352-a5ee-4f54-a17e-dc796256864d/12306-0
00:55:43.590 --> 00:55:44.390
No, it's fine.

bda32352-a5ee-4f54-a17e-dc796256864d/12329-0
00:55:44.460 --> 00:55:48.664
I mean this is this the the math
was all in making each of these

bda32352-a5ee-4f54-a17e-dc796256864d/12329-1
00:55:48.664 --> 00:55:50.280
individual models, right?

bda32352-a5ee-4f54-a17e-dc796256864d/12373-0
00:55:50.350 --> 00:55:53.513
It's it's before the averaging
and then so if if you had some

bda32352-a5ee-4f54-a17e-dc796256864d/12336-0
00:55:50.680 --> 00:55:50.840
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/12373-1
00:55:53.513 --> 00:55:56.522
other sort of combination you
want Madden, maybe we should

bda32352-a5ee-4f54-a17e-dc796256864d/12373-2
00:55:56.522 --> 00:55:59.685
have this conversation later
because this is I think a really

bda32352-a5ee-4f54-a17e-dc796256864d/12373-3
00:55:59.685 --> 00:56:01.980
interesting topic that's after
the sampling.

bda32352-a5ee-4f54-a17e-dc796256864d/12394-0
00:56:02.150 --> 00:56:04.515
So that's after you've taken
these six different models and

bda32352-a5ee-4f54-a17e-dc796256864d/12396-0
00:56:04.410 --> 00:56:04.570
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/12394-1
00:56:04.515 --> 00:56:05.460
you've sampled for them.

bda32352-a5ee-4f54-a17e-dc796256864d/12408-0
00:56:05.470 --> 00:56:08.600
So none of the cross fading,
transitioning stuff blows up.

bda32352-a5ee-4f54-a17e-dc796256864d/12432-0
00:56:08.690 --> 00:56:10.782
It also doesn't blow up your
ability to calculate the

bda32352-a5ee-4f54-a17e-dc796256864d/12432-1
00:56:10.782 --> 00:56:13.067
marginal likelihood that just
the question is, do you need

bda32352-a5ee-4f54-a17e-dc796256864d/12432-2
00:56:13.067 --> 00:56:13.260
that?

bda32352-a5ee-4f54-a17e-dc796256864d/12458-0
00:56:13.270 --> 00:56:16.091
Is that actually gonna be part
of the averaging that you end up

bda32352-a5ee-4f54-a17e-dc796256864d/12458-1
00:56:16.091 --> 00:56:17.060
that you end up doing?

bda32352-a5ee-4f54-a17e-dc796256864d/12460-0
00:56:18.120 --> 00:56:18.910
Hey, I'll send you.

bda32352-a5ee-4f54-a17e-dc796256864d/12470-0
00:56:18.920 --> 00:56:20.290
I'll send you a couple of
papers.

bda32352-a5ee-4f54-a17e-dc796256864d/12498-0
00:56:20.300 --> 00:56:24.324
I'll send you Warners and
Andreas and yeah, like, I mean,

bda32352-a5ee-4f54-a17e-dc796256864d/12498-1
00:56:24.324 --> 00:56:28.695
in this particular case, I think
it would come up with a worse

bda32352-a5ee-4f54-a17e-dc796256864d/12498-2
00:56:28.695 --> 00:56:29.180
answer.

bda32352-a5ee-4f54-a17e-dc796256864d/12517-0
00:56:29.980 --> 00:56:33.533
Uh, but the question is, in most
cases, does it come up with

bda32352-a5ee-4f54-a17e-dc796256864d/12517-1
00:56:33.533 --> 00:56:34.930
better or worse answers?

bda32352-a5ee-4f54-a17e-dc796256864d/12529-0
00:56:34.940 --> 00:56:35.680
So yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/12593-0
00:56:35.560 --> 00:56:39.084
And and I I think that is really
the question and I think it's

bda32352-a5ee-4f54-a17e-dc796256864d/12593-1
00:56:39.084 --> 00:56:42.719
really hard to answer because we
don't know idea how the fix the

bda32352-a5ee-4f54-a17e-dc796256864d/12593-2
00:56:42.719 --> 00:56:46.298
things we might try compare to
what the actual the actual thing

bda32352-a5ee-4f54-a17e-dc796256864d/12593-3
00:56:46.298 --> 00:56:49.877
is of course there is no actual
actual thing because right, but

bda32352-a5ee-4f54-a17e-dc796256864d/12593-4
00:56:49.877 --> 00:56:53.344
it's easy for us to have this
conversation about, well, these

bda32352-a5ee-4f54-a17e-dc796256864d/12572-0
00:56:50.400 --> 00:56:50.630
Right.

bda32352-a5ee-4f54-a17e-dc796256864d/12593-5
00:56:53.344 --> 00:56:56.140
are the ones that were closer to
the input model.

bda32352-a5ee-4f54-a17e-dc796256864d/12628-0
00:56:56.150 --> 00:56:58.108
These the ones are from the
input model, but that's only

bda32352-a5ee-4f54-a17e-dc796256864d/12628-1
00:56:58.108 --> 00:57:00.169
because this is a game that we
made up and then we would we

bda32352-a5ee-4f54-a17e-dc796256864d/12628-2
00:57:00.169 --> 00:57:01.130
have no way of knowing that.

bda32352-a5ee-4f54-a17e-dc796256864d/12645-0
00:57:01.580 --> 00:57:04.512
And in fact, we should say that
explicitly the right this is a

bda32352-a5ee-4f54-a17e-dc796256864d/12645-1
00:57:04.512 --> 00:57:04.930
relative.

bda32352-a5ee-4f54-a17e-dc796256864d/12653-0
00:57:04.970 --> 00:57:07.880
These probabilities or statement
of relative fitness right?

bda32352-a5ee-4f54-a17e-dc796256864d/12660-0
00:57:08.030 --> 00:57:08.120
Yes.

bda32352-a5ee-4f54-a17e-dc796256864d/12665-0
00:57:08.130 --> 00:57:10.960
All six of these models could
absolutely suck, right?

bda32352-a5ee-4f54-a17e-dc796256864d/12675-0
00:57:11.050 --> 00:57:12.740
They could be nothing like the
wheel thing.

bda32352-a5ee-4f54-a17e-dc796256864d/12685-0
00:57:12.750 --> 00:57:14.920
They could all be terrible,
terrible things.

bda32352-a5ee-4f54-a17e-dc796256864d/12692-0
00:57:14.970 --> 00:57:17.180
You would still get this
relative plausibility.

bda32352-a5ee-4f54-a17e-dc796256864d/12708-0
00:57:17.190 --> 00:57:20.061
It's just saying you gave me a
word that consists of these six

bda32352-a5ee-4f54-a17e-dc796256864d/12708-1
00:57:20.061 --> 00:57:20.380
models.

bda32352-a5ee-4f54-a17e-dc796256864d/12726-0
00:57:20.390 --> 00:57:22.215
These are the relative
probabilities we assigned to

bda32352-a5ee-4f54-a17e-dc796256864d/12726-1
00:57:22.215 --> 00:57:22.390
them.

bda32352-a5ee-4f54-a17e-dc796256864d/12755-0
00:57:23.290 --> 00:57:25.976
Alright, we have decided
advantage in the forecasting

bda32352-a5ee-4f54-a17e-dc796256864d/12755-1
00:57:25.976 --> 00:57:29.160
World Network playing a temporal
game and so there's data still

bda32352-a5ee-4f54-a17e-dc796256864d/12755-2
00:57:29.160 --> 00:57:30.900
to come that we can look at
later.

bda32352-a5ee-4f54-a17e-dc796256864d/12760-0
00:57:30.990 --> 00:57:32.210
But yeah, I agree with you.

bda32352-a5ee-4f54-a17e-dc796256864d/12765-0
00:57:32.220 --> 00:57:32.860
What you're saying?

bda32352-a5ee-4f54-a17e-dc796256864d/12767-0
00:57:32.870 --> 00:57:33.040
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/12786-0
00:57:33.080 --> 00:57:36.100
OK, I'll send you the papers and
really, really interesting talk.

bda32352-a5ee-4f54-a17e-dc796256864d/12785-0
00:57:34.810 --> 00:57:35.030
2.

bda32352-a5ee-4f54-a17e-dc796256864d/12786-1
00:57:36.100 --> 00:57:36.420
Thanks.

bda32352-a5ee-4f54-a17e-dc796256864d/12797-0
00:57:39.770 --> 00:57:43.370
Your questions online are in the
room, Steve.

bda32352-a5ee-4f54-a17e-dc796256864d/12808-0
00:57:43.460 --> 00:57:45.610
I thought first of all, Sarah,
amazing talk.

bda32352-a5ee-4f54-a17e-dc796256864d/12826-0
00:57:45.620 --> 00:57:48.753
You are a master giving a talk
and I love the use of feline

bda32352-a5ee-4f54-a17e-dc796256864d/12826-1
00:57:48.753 --> 00:57:49.170
imagery.

bda32352-a5ee-4f54-a17e-dc796256864d/12841-0
00:57:49.980 --> 00:57:52.350
I knew in the dog party that was
not your house.

bda32352-a5ee-4f54-a17e-dc796256864d/12840-0
00:57:50.180 --> 00:57:50.540
Thank you.

bda32352-a5ee-4f54-a17e-dc796256864d/12850-0
00:57:52.360 --> 00:57:53.290
That was probably suits.

bda32352-a5ee-4f54-a17e-dc796256864d/12902-0
00:57:53.660 --> 00:57:58.330
So I my question is also pretend
to this and so you said that all

bda32352-a5ee-4f54-a17e-dc796256864d/12902-1
00:57:58.330 --> 00:58:02.575
these models could be wrong and
this is A1 dimensional slip

bda32352-a5ee-4f54-a17e-dc796256864d/12902-2
00:58:02.575 --> 00:58:07.032
model and you've selected the
2nd and the 3rd over as the most

bda32352-a5ee-4f54-a17e-dc796256864d/12902-3
00:58:07.032 --> 00:58:11.630
likely based on your analytical
and that's how you weigh things.

bda32352-a5ee-4f54-a17e-dc796256864d/12915-0
00:58:12.160 --> 00:58:14.260
But what about waiting from
additional information?

bda32352-a5ee-4f54-a17e-dc796256864d/12946-0
00:58:14.270 --> 00:58:17.536
What if you knew from some kind
of three dimensional velocity

bda32352-a5ee-4f54-a17e-dc796256864d/12946-1
00:58:17.536 --> 00:58:20.854
inversion or moral information,
or something else that default

bda32352-a5ee-4f54-a17e-dc796256864d/12946-2
00:58:20.854 --> 00:58:21.960
dipped a certain way?

bda32352-a5ee-4f54-a17e-dc796256864d/12959-0
00:58:21.970 --> 00:58:24.544
Or there was a certain
compliance structure of velocity

bda32352-a5ee-4f54-a17e-dc796256864d/12959-1
00:58:24.544 --> 00:58:25.600
structure in the crust.

bda32352-a5ee-4f54-a17e-dc796256864d/12974-0
00:58:25.680 --> 00:58:28.793
How do you impose independent
data constraints in a model like

bda32352-a5ee-4f54-a17e-dc796256864d/12974-1
00:58:28.793 --> 00:58:29.040
this?

bda32352-a5ee-4f54-a17e-dc796256864d/12993-0
00:58:29.470 --> 00:58:32.579
To more fully sample the
ensemble of Lightning models,

bda32352-a5ee-4f54-a17e-dc796256864d/12993-1
00:58:32.579 --> 00:58:34.500
including in the third
dimension.

bda32352-a5ee-4f54-a17e-dc796256864d/13006-0
00:58:36.820 --> 00:58:40.980
Right, so so none of this
requires 1 dimensionality.

bda32352-a5ee-4f54-a17e-dc796256864d/13040-0
00:58:40.990 --> 00:58:44.327
This is this was just to make
something that you could view

bda32352-a5ee-4f54-a17e-dc796256864d/13021-0
00:58:41.620 --> 00:58:41.850
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13066-0
00:58:43.060 --> 00:58:47.258
So I I assume that but it gets
pretty complicated very soon and

bda32352-a5ee-4f54-a17e-dc796256864d/13040-1
00:58:44.327 --> 00:58:45.050
easily, yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13053-0
00:58:47.180 --> 00:58:47.460
Right.

bda32352-a5ee-4f54-a17e-dc796256864d/13066-1
00:58:47.258 --> 00:58:51.258
it can still solve analytically
and help focus your modeling

bda32352-a5ee-4f54-a17e-dc796256864d/13107-0
00:58:50.440 --> 00:58:54.471
Yes, because this is I mean, OK,
so as long to talk about the new

bda32352-a5ee-4f54-a17e-dc796256864d/13066-2
00:58:51.258 --> 00:58:51.520
and.

bda32352-a5ee-4f54-a17e-dc796256864d/13107-1
00:58:54.471 --> 00:58:57.953
elasticity then then you are
talking about the d = m * M

bda32352-a5ee-4f54-a17e-dc796256864d/13107-2
00:58:57.953 --> 00:59:01.434
problem and it has this
conjugate prior and all the math

bda32352-a5ee-4f54-a17e-dc796256864d/13107-3
00:59:01.434 --> 00:59:02.350
is fine, right?

bda32352-a5ee-4f54-a17e-dc796256864d/13123-0
00:59:02.400 --> 00:59:04.422
When you're talking about like,
oh, well, what if it's 3D

bda32352-a5ee-4f54-a17e-dc796256864d/13123-1
00:59:04.422 --> 00:59:04.770
structure?

bda32352-a5ee-4f54-a17e-dc796256864d/13138-0
00:59:04.770 --> 00:59:07.009
Whatever that you're just
changing the form of G, it's

bda32352-a5ee-4f54-a17e-dc796256864d/13138-1
00:59:07.009 --> 00:59:07.700
that same matrix.

bda32352-a5ee-4f54-a17e-dc796256864d/13165-0
00:59:07.710 --> 00:59:12.112
The math is all the same, umm
and and of course my these are

bda32352-a5ee-4f54-a17e-dc796256864d/13144-0
00:59:09.100 --> 00:59:09.240
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13165-1
00:59:12.112 --> 00:59:15.070
variations that I made just for
funzies.

bda32352-a5ee-4f54-a17e-dc796256864d/13224-0
00:59:15.220 --> 00:59:18.613
If you had some some reason to,
you know, but, and they'll based

bda32352-a5ee-4f54-a17e-dc796256864d/13224-1
00:59:18.613 --> 00:59:21.902
on absolutely nothing other than
hey, here was a six different

bda32352-a5ee-4f54-a17e-dc796256864d/13224-2
00:59:21.902 --> 00:59:25.295
things that might be fun to plot
if you had good reason to think

bda32352-a5ee-4f54-a17e-dc796256864d/13224-3
00:59:25.295 --> 00:59:28.426
about specific other things,
right, you should do that also

bda32352-a5ee-4f54-a17e-dc796256864d/13224-4
00:59:28.426 --> 00:59:31.610
if you have reason to believe
different things off priority.

bda32352-a5ee-4f54-a17e-dc796256864d/13230-0
00:59:31.790 --> 00:59:33.890
I'm there was a place to put
things in.

bda32352-a5ee-4f54-a17e-dc796256864d/13252-0
00:59:34.480 --> 00:59:38.147
Ah, so it doesn't necessarily
apply so much to this thing that

bda32352-a5ee-4f54-a17e-dc796256864d/13252-1
00:59:38.147 --> 00:59:39.310
we're talking about.

bda32352-a5ee-4f54-a17e-dc796256864d/13350-0
00:59:39.320 --> 00:59:42.631
But if for example, you know one
of the things we were talking

bda32352-a5ee-4f54-a17e-dc796256864d/13350-1
00:59:42.631 --> 00:59:45.889
about was earthquake location,
you would probably assume that

bda32352-a5ee-4f54-a17e-dc796256864d/13350-2
00:59:45.889 --> 00:59:49.148
you're all priority location is
pretty good and it could have

bda32352-a5ee-4f54-a17e-dc796256864d/13350-3
00:59:49.148 --> 00:59:52.353
some Airways on it, but they're
unlikely to be large, so you

bda32352-a5ee-4f54-a17e-dc796256864d/13350-4
00:59:52.353 --> 00:59:55.559
wouldn't necessarily be like,
ohh isn't my earthquake key or

bda32352-a5ee-4f54-a17e-dc796256864d/13350-5
00:59:55.559 --> 00:59:58.712
he or he or he or with equal
probability you'll probably be

bda32352-a5ee-4f54-a17e-dc796256864d/13350-6
00:59:58.712 --> 01:00:02.128
like it's probably heal like you
probably for the Gaussian prior

bda32352-a5ee-4f54-a17e-dc796256864d/13350-7
01:00:02.128 --> 01:00:04.860
on it and be like, well, I'm
pretty sure it's here.

bda32352-a5ee-4f54-a17e-dc796256864d/13354-0
01:00:04.950 --> 01:00:05.720
I'm less likely.

bda32352-a5ee-4f54-a17e-dc796256864d/13362-0
01:00:05.730 --> 01:00:06.680
That's yours, like here.

bda32352-a5ee-4f54-a17e-dc796256864d/13379-0
01:00:06.730 --> 01:00:11.396
And so this purple is actually
the marginal likelihood times

bda32352-a5ee-4f54-a17e-dc796256864d/13379-1
01:00:11.396 --> 01:00:12.160
the prior.

bda32352-a5ee-4f54-a17e-dc796256864d/13397-0
01:00:12.170 --> 01:00:15.303
And so your prior would tell you
what things you think are likely

bda32352-a5ee-4f54-a17e-dc796256864d/13397-1
01:00:15.303 --> 01:00:15.920
and unlikely.

bda32352-a5ee-4f54-a17e-dc796256864d/13411-0
01:00:16.640 --> 01:00:19.810
OK, so so so data does matter in
that sense.

bda32352-a5ee-4f54-a17e-dc796256864d/13418-0
01:00:19.820 --> 01:00:22.010
Back to Sue's question, it
matters a lot.

bda32352-a5ee-4f54-a17e-dc796256864d/13425-0
01:00:22.020 --> 01:00:23.270
And determining your priors.

bda32352-a5ee-4f54-a17e-dc796256864d/13432-0
01:00:23.490 --> 01:00:24.380
Yeah, yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13449-0
01:00:25.090 --> 01:00:29.016
Well, yes, I mean and and also
like you would incorporate that

bda32352-a5ee-4f54-a17e-dc796256864d/13449-1
01:00:29.016 --> 01:00:29.390
right?

bda32352-a5ee-4f54-a17e-dc796256864d/13476-0
01:00:29.400 --> 01:00:31.840
Like if if you have subsurface
information, you'd put that in

bda32352-a5ee-4f54-a17e-dc796256864d/13463-0
01:00:29.990 --> 01:00:30.700
Absolutely, yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13476-1
01:00:31.840 --> 01:00:34.200
your Greens functions matrix and
it would already be there.

bda32352-a5ee-4f54-a17e-dc796256864d/13474-0
01:00:33.430 --> 01:00:33.620
And.

bda32352-a5ee-4f54-a17e-dc796256864d/13478-0
01:00:35.610 --> 01:00:36.060
OK.

bda32352-a5ee-4f54-a17e-dc796256864d/13481-0
01:00:36.070 --> 01:00:36.520
Thank you.

bda32352-a5ee-4f54-a17e-dc796256864d/13483-0
01:00:36.590 --> 01:00:36.870
Thank you.

bda32352-a5ee-4f54-a17e-dc796256864d/13494-0
01:00:38.990 --> 01:00:39.490
Other questions?

bda32352-a5ee-4f54-a17e-dc796256864d/13497-0
01:00:39.400 --> 01:00:41.750
But but you will always have
holes, right?

bda32352-a5ee-4f54-a17e-dc796256864d/13514-0
01:00:41.760 --> 01:00:44.022
Because you don't have perfect
information about the subsurface

bda32352-a5ee-4f54-a17e-dc796256864d/13514-1
01:00:44.022 --> 01:00:44.940
everywhere, you'd be like.

bda32352-a5ee-4f54-a17e-dc796256864d/13536-0
01:00:44.950 --> 01:00:46.806
Well, I know it's healed, but
then I don't know what it's

bda32352-a5ee-4f54-a17e-dc796256864d/13536-1
01:00:46.806 --> 01:00:47.350
doing over there.

bda32352-a5ee-4f54-a17e-dc796256864d/13532-0
01:00:48.260 --> 01:00:48.470
Yeah.

bda32352-a5ee-4f54-a17e-dc796256864d/13561-0
01:00:48.480 --> 01:00:50.952
And also you could use this to
decide what polls matter the

bda32352-a5ee-4f54-a17e-dc796256864d/13561-1
01:00:50.952 --> 01:00:53.423
most and what new data you
should collect to constrain your

bda32352-a5ee-4f54-a17e-dc796256864d/13561-2
01:00:53.423 --> 01:00:53.670
model.

bda32352-a5ee-4f54-a17e-dc796256864d/13565-0
01:00:53.680 --> 01:00:53.860
Better.

bda32352-a5ee-4f54-a17e-dc796256864d/13573-0
01:00:54.570 --> 01:00:55.010
Absolutely.

bda32352-a5ee-4f54-a17e-dc796256864d/13571-0
01:00:55.090 --> 01:00:56.160
Fighting the mediums.

bda32352-a5ee-4f54-a17e-dc796256864d/13575-0
01:00:56.170 --> 01:00:56.940
Yeah, great. Thanks.

bda32352-a5ee-4f54-a17e-dc796256864d/13583-0
01:01:00.510 --> 01:01:01.070
Other questions?

bda32352-a5ee-4f54-a17e-dc796256864d/13602-0
01:01:05.150 --> 01:01:10.480
Uh, if not, let's all think
Sarah, for a fantastic talk.

bda32352-a5ee-4f54-a17e-dc796256864d/13605-0
01:01:12.470 --> 01:01:13.580
Thank you everyone.

bda32352-a5ee-4f54-a17e-dc796256864d/13612-0
01:01:14.000 --> 01:01:15.790
Math apologizes for all the
math.