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Structural Equation Modeling (SEM) is a key framework in causal inference. As I’m diving deeper and deeper into these topics to teach them and, well, finally understand them, I was delighted to host Ed Merkle on the show.
A professor of psychological sciences at the University of Missouri, Ed discusses his work on Bayesian applications to psychometric models and model estimation, particularly in the context of Bayesian SEM. He explains the importance of BSEM in psychometrics and the challenges encountered in its estimation.
Ed also introduces his blavaan package in R, which enhances researchers’ capabilities in BSEM and has been instrumental in the dissemination of these methods. Additionally, he explores the role of Bayesian methods in forecasting and crowdsourcing wisdom.
When he’s not thinking about stats and psychology, Ed can be found running, playing the piano, or playing 8-bit video games.
Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !
Thank you to my Patrons for making this episode possible!
Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio.
Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag 😉
Takeaways:
– Bayesian SEM is a powerful framework in psychometrics that allows for the estimation of complex models involving multiple variables and causal relationships.
– Understanding the principles of Bayesian inference is crucial for effectively applying Bayesian SEM in psychological research.
– Informative priors play a key role in Bayesian modeling, providing valuable information and improving the accuracy of model estimates.
– Challenges in BSEM estimation include specifying appropriate prior distributions, dealing with unidentified parameters, and ensuring convergence of the model. Incorporating prior information is crucial in Bayesian modeling, especially when dealing with large models and imperfect data.
– The blavaan package enhances researchers’ capabilities in Bayesian structural equation modeling, providing a user-friendly interface and compatibility with existing frequentist models.
– Bayesian methods offer advantages in forecasting and subjective probability by allowing for the characterization of uncertainty and providing a range of predictions.
– Interpreting Bayesian model results requires careful consideration of the entire posterior distribution, rather than focusing solely on point estimates.
– Latent variable models, also known as structural equation models, play a crucial role in psychometrics, allowing for the estimation of unobserved variables and their influence on observed variables.
– The speed of MCMC estimation and the need for a slower, more thoughtful workflow are common challenges in the Bayesian workflow.
– The future of Bayesian psychometrics may involve advancements in parallel computing and GPU-accelerated MCMC algorithms.
Chapters:
00:00 Introduction to the Conversation
02:17 Background and Work on Bayesian SEM
04:12 Topics of Focus: Structural Equation Models
05:16 Introduction to Bayesian Inference
09:30 Importance of Bayesian SEM in Psychometrics
10:28 Overview of Bayesian Structural Equation Modeling (BSEM)
12:22 Relationship between BSEM and Causal Inference
15:41 Advice for Learning BSEM
21:57 Challenges in BSEM Estimation
34:40 The Impact of Model Size and Data Quality
37:07 The Development of the Blavaan Package
42:16 Bayesian Methods in Forecasting and Subjective Probability
46:27 Interpreting Bayesian Model Results
51:13 Latent Variable Models in Psychometrics
56:23 Challenges in the Bayesian Workflow
01:01:13 The Future of Bayesian Psychometrics
Links from the show:
- Ed’s website: https://ecmerkle.github.io/
- Ed on Mastodon: https://mastodon.sdf.org/@edgarmerkle
- Ed on BlueSky: @edgarmerkle.bsky.social
- Ed on GitHub: https://github.com/ecmerkle
- blaavan R package: https://ecmerkle.github.io/blavaan/
- Resources on how to use blaavan: https://ecmerkle.github.io/blavaan/articles/resources.html
- Richard McElreath, Table 2 Fallacy: https://youtu.be/uanZZLlzKHw?si=vssrwJsvGO5HhH5H&t=4323
Transcript
This is an automatic transcript and may therefore contain errors. Please get in touch if you’re willing to correct them.
Transcript
Structural Equation Modeling, or SEM, is a
key framework in causal inference.
2
As I'm diving deeper and deeper into these
topics to teach them and, well, finally
3
understand them, I was delighted to host
Ed Merkel on the show.
4
A professor of psychological sciences at
the University of Missouri, Ed discusses
5
his work on Bayesian applications to
psychometric models and model estimation.
6
particularly in the context of Bayesian
SEM.
7
He explains the importance of Bayesian SEM
in psychometrics and the challenges
8
encountered in its estimation.
9
Ed also introduces his blaavan package in
R, which enhances researchers'
10
capabilities in Bayesian SEM and has been
instrumental in the dissemination of these
11
methods.
12
Additionally, he explores the role of
Bayesian methods in forecasting and
13
crowdsourcing wisdom, and when he's not
thinking about stats and psychology, Ed
14
can be found running, playing the piano,
or playing 8 -bit video games.
15
This is Learning Bayesian Statistics,
episode 102, recorded February 14, 2024.
16
Welcome to Learning Bayesian Statistics, a
podcast about Bayesian inference, the
17
methods, the projects, and the people who
make it possible.
18
I'm your host, Alex Andorra.
19
You can follow me on Twitter at alex
-underscore -andorra.
20
like the country.
21
For any info about the show, learnbasedats
.com is left last to be.
22
Show notes, becoming a corporate sponsor,
unlocking Bayesian Merge, supporting the
23
show on Patreon, everything is in there.
24
That's learnbasedats .com.
25
If you're interested in one -on -one
mentorship, online courses, or statistical
26
consulting, feel free to reach out and
book a call at topmate .io slash alex
27
underscore and dora.
28
See you around, folks, and best Bayesian
wishes to you all.
29
Thank you for having me.
30
Yeah, you bet.
31
Thanks a lot for taking the time.
32
I am really happy to have you on and I
have a lot of questions.
33
So that is perfect.
34
Before that, as usual, how would you
define the work you're doing nowadays and
35
how did you end up working on this?
36
Well, a lot of my work right now is with
37
Bayesian applications to psychometric
models and model estimation.
38
Over time, I've gotten more and more into
the model estimation and computation as
39
opposed to applications.
40
And it was a slow process to get here.
41
I started doing some Bayesian modeling
when I was working on my PhD.
42
I finished that in 2005 and...
43
I felt a bit restricted by what I could do
with the tools I had at that time, but
44
things have improved a lot since then.
45
And also I've learned a lot since then.
46
So I have over time left some things and
come back to them.
47
And when I come back to them, I find
there's more progress that can be made.
48
Yeah, that makes sense.
49
And that's always super...
50
interesting and inspiring to see such
diverse backgrounds on the show.
51
I'm always happy to see that.
52
And by the way, thanks a lot to Jorge
Sinval to do the introduction.
53
Today is February 14th and he was our
matchmaker.
54
So thanks a lot, Jorge.
55
And yeah, like this promises to be a great
episode.
56
So thanks a lot for the suggestion.
57
And Ed, actually, could you tell us the
topics that you are particularly focusing
58
on?
59
Yeah, recently, so in psychology,
psychometrics, education, there's this
60
class of models, structural equation
models.
61
It's a pretty large class of models and I
think some special cases have been really
62
useful.
63
Others sometimes get a bad reputation
with, I think, certain groups of
64
statistics people.
65
But it's this big class and it has
interested me for a long time because so
66
much can be done with this class of
models.
67
So the Bayesian estimation part has
especially been interesting to me because
68
it was relatively underexplored for a long
time.
69
And there's some unique challenges there
that I have found and I've tried to make
70
some progress on.
71
Yeah.
72
And we're going to dive into these topics
for sure in the coming minutes.
73
But to still talk about your background,
do you remember how you first got
74
introduced to Bayesian inference and also
why they sticked with you?
75
Yes.
76
I think part of how I got interested in
Bayesian inference,
77
starts a lot earlier to when I was growing
up.
78
I'm about the age where the first half of
my childhood, there were no computers.
79
And the second half of growing up,
computers were in people's houses, the
80
internet was coming around and so on.
81
So I grew up with having a computer in my
house for the first time.
82
And then...
83
just messing around with it and learning
how to do things on it.
84
So then later, a while later when I was
working on my PhD, I grew up with the
85
computing topics and I enjoyed that.
86
So I felt at the time with Bayesian
estimation, some of the interesting
87
computing things were coming out around
the time I was working on my PhD.
88
So for example, wind bugs was a big thing,
say around 2000, 2001 or so.
89
That was when I was starting to work on my
PhD.
90
And that seemed like a fun little program
where you could build these models and do
91
some Bayesian estimation.
92
At the time, I didn't always know exactly
what I was doing, but I still found it
93
interesting and perhaps a bit more
intuitive than some of the other.
94
methods that were out there at the time.
95
Yeah.
96
And actually it seems like you've been
part of that movement, which introduced
97
patient stats a lot in the psychological
sciences.
98
Can you elaborate on the role of the
patient framework in psychological
99
research?
100
Always a hard word to say when you have a
French accent.
101
I understand.
102
So yeah, when I was working on my PhD, I
think there was not a lot of psychology
103
applications necessarily, or maybe it was
just in certain areas.
104
So when I started on my PhD, I was doing
like some cognitive psychology modeling
105
where you would bring.
106
someone into a room for an experiment and
it could be about memory or something
107
where you have them remember a list of
words and then you give them a new list of
108
words and ask them which did you see
before and which are new and then you can
109
model people's response times or accuracy.
110
So there were some Bayesian applications
definitely related to like memory modeling
111
at that time but more generally there were
less applications.
112
I did my PhD on some Bayesian structural
equation modeling applications to missing
113
data.
114
At the time, I had a really hard time
publishing that work.
115
I think it was partly because I just
wasn't that great at writing papers at the
116
time, but also there weren't as many
Bayesian applications.
117
So I think people were less interested.
118
But over time that has changed, I think
with...
119
with improved tools and more attention to
Bayesian modeling.
120
You see it more and more in psychology.
121
Sometimes it's just an alternative to
frequentness.
122
Like if you're doing a regression or a
mixed model, Bayesian is just an
123
alternative.
124
Other times, like for the structural
equation models, there can be some
125
advantages to the Bayesian approach,
especially related to characterizing
126
uncertainty.
127
And so I think there's more and more
attention in psychology and psychometrics
128
to some of those issues.
129
Yeah.
130
And definitely interesting to see, to hear
that the publishing has, has gotten, has
131
become easier, at least for you.
132
And a method you're especially working on
and developing is Bayesian structural
133
equation modeling or BSEM.
134
So we've never covered that yet on the
show.
135
So could you give our listeners a primer
on BSEM and its importance in
136
psychometrics?
137
Yes.
138
So this Bayesian structural equation
modeling framework, or maybe I can start
139
with just the structural equation modeling
part, that overlaps with lots of other
140
modeling frameworks.
141
So item response models and factor
analysis models, these are more on the
142
measurement side, examining how say some
tests or scales help us to measure a
143
person's aptitude.
144
Those could all be viewed as special cases
of structural equation models, but the
145
heart of structural equation models
involves,
146
Like a series of regression models all in
in one big model.
147
So if if you know, like the directed
acyclic graphs that come from causal
148
research, especially Judea Pearl, you can
think of structural equation models as a
149
way to estimate those types of models.
150
Like these graphs will often have many
variables.
151
and you have arrows between variables that
reflect some causal relationships.
152
Well, now structural equation models are
throwing likelihoods on top of that,
153
typically normal likelihoods.
154
And that gives us a way to fit these sorts
of models to data.
155
Whereas directed acyclic graph would
often, you look at that and that helps you
156
to know what is estimable and what is not
estimable, say.
157
that now the structural equation model is
a way to fit that sort of thing to data.
158
But it also overlaps with mixed models.
159
Like I said, the item response models,
there's some ideas related to principal
160
components in there.
161
It overlaps with a lot of things.
162
Yeah, that's really interesting to have
that take you on structural.
163
structural equation modeling and the
relationship to causal inference in a way.
164
And so as you were saying, it also relates
to UDA pearls, to calculus and things like
165
that.
166
So I definitely encourage the listener to
dive deeper on these literature that's
167
absolutely fascinating.
168
I really love that.
169
And that's also from my own perspective
learning about those
170
things recently, I found that it was way
easier being already a Bayesian.
171
If you already do Bayesian models from a
generative modeling perspective, then
172
intervening on the graph and doing, like
in calculus, doing an intervention is
173
basically like doing bus operative
sampling as you were already doing on your
174
Bayesian model.
175
But instead of having already
176
conditioned on some data, you come up with
the platonic idea of the data generative
177
model that you have in mind.
178
And then you intervene on the model by
setting some values on some of the nodes
179
and then seeing what that gives you, what
that intervention gives you on the
180
outcome.
181
And I find that really, really natural to
learn already from a Bayesian perspective.
182
I don't know what your experience has
been.
183
Oh, yeah, I think the Bayesian perspective
really helps you keep these models at like
184
the raw data level.
185
So you're thinking about how do individual
variables cause other variables and what
186
does that mean about data predictions?
187
If you look at often how frequent this
present these models.
188
We have something like random effects in
these models.
189
And so from a frequentist perspective, you
wanna get rid of those random effects,
190
marginalize them out of a model.
191
And then for these models, we're left with
some structured covariance matrix.
192
And often the frequentist will start with,
okay, you have an observed covariance
193
matrix and then our model implies a
covariance matrix.
194
But I find that so it's...
195
it's unintuitive to think about compared
to raw data.
196
You know, like I can see how the data from
one variable can influence another
197
variable, but now to think about what does
that mean about the prediction for a
198
covariance that I think makes it less
intuitive and that's really where some of
199
the Bayesian models have an advantage.
200
Yeah, yeah, definitely.
201
And that's why my learning myself on
202
on this front and also teaching about
these topics has been extremely helpful
203
for myself because to teach it, you really
have to understand it really well.
204
So that was a great Or said differently
that you don't understand it until you
205
teach it.
206
I've thought that I understood things
before, but then when I teach it, I
207
realized, well, I didn't quite understand
everything.
208
Yeah, for sure.
209
Definitely.
210
And what advice would you give to someone
who is already a Bayesian and want to
211
learn about these structural equation
modeling, and to someone who is already
212
doing psychometrics and would like to now
learn about these structural equation
213
modeling?
214
What advice would you give to help them
start on this path?
215
Yeah, I think.
216
For people who already know Bayesian
models.
217
I think I would explain structural
equation models as like a combination of
218
say principal components or factor
analysis and then regression.
219
And I think you can, there's these
expressions for the structural equation
220
modeling framework where you have these
big matrices and depending on what goes in
221
the matrices, you get certain models.
222
I would almost advise against starting
there because you can have this giant
223
framework that's expressing matrices, but
it gets very confusing about what goes in
224
what matrix or what does this mean from a
general perspective.
225
I would almost advise starting smaller,
say with some factor analysis models, or
226
you can have these models where there's
one unobserved variable regressed on
227
another unobserved variable.
228
I would say like starting with some of
those models and then working your way up.
229
On the other hand, if someone already
knows the psychometric models and is
230
moving to Bayesian modeling, I think the
challenge is to think of these models
231
again as models of data, not as models of
a covariance matrix.
232
I guess that's related to what we talked
about earlier.
233
But if you know the frequentist models,
typically the
234
just how they talk about these models
involves just a covariance matrix or
235
tricks for marginalizing over the random
effects or the random parameters in the
236
model.
237
And I think taking a step back and looking
at what does the model say about the data
238
before we try to get rid of these random
parameters, I think that is helpful for
239
thinking through the Bayesian approach.
240
Okay, yeah.
241
Yeah, super interesting.
242
in the then I would also want to ask you
once you once you've done that so once
243
you're into BSEM why is that useful and
what is its importance in your field of
244
psychometrics these days?
245
Yeah, so the Bayesian part, I would say
one use is, I think it slows you down a
246
bit.
247
There are certain, say, specifying prior
distributions and really thinking through
248
the prior distributions.
249
This is something you don't encounter on
the frequentist side.
250
It's going to slow you down, but I think
for these models, that ends up being
251
useful because...
252
You know, if you simulate data from priors
and really look at what are these priors
253
saying about the sort of data I can
expect, I find that helps you understand
254
these models in a way that you don't often
get from the frequentist side.
255
And then I guess said differently, I think
over say the past 30, 40 years with these
256
structural equation models, I think often
in the field we've come to expect that I
257
can specify this giant model and hit a
button and run it.
258
And then I get some results and report
just a few results from this big model.
259
I think we've lost something with
understanding what.
260
exactly as this model is saying about the
data.
261
And that's a place where the Bayesian
versions of these models can be really
262
helpful.
263
I think there was a second part to your
question, but I forgot the second part.
264
Yeah, what is the importance of BSCM these
days in psychometrics?
265
Yeah, yeah.
266
I think there's a couple, I think key
advantages.
267
One, again, we have random parameters that
are sort of like random effects if you
268
know mixed models.
269
And with MCMC, we can sample these
parameters and characterize their
270
uncertainty or allow the uncertainty in
these random parameters to filter through
271
to other model predictions.
272
That's something that's very natural to do
from a Bayesian perspective.
273
potentially not from other perspectives.
274
So there's a random parameter piece.
275
Another thing that people talk about a lot
is fitting these models to smaller sample
276
sizes.
277
So for some of these structural equation
models, there's a lot happening and you
278
can get these failures to converge if
you're estimating frequentist versions of
279
the model.
280
Bayesian models,
281
can still work there.
282
I think you still have to be careful
because of course if you don't have much
283
data, the priors are going to be more
influential and sensitivity analyses and
284
things become very important.
285
So I think it's not just a full solution
to if you don't have much data, but I
286
think you can make some progress there
with Bayesian models that are maybe more
287
difficult with frequentist models.
288
Okay, I see.
289
And on the other end, what are some of the
biggest challenges you've encountered in
290
BSM estimation and how does your work
address them?
291
I've found I encounter problems as I'm
working on my R package or just
292
unestimating the models.
293
There's a number of problems that aren't
completely evident when you start.
294
And one I've worked on recently and I
continue to work on is specifying prior
295
distributions for these models in a way
that you know exactly what the prior
296
distributions are.
297
in a non -software dependent way.
298
So in some of these models, there's, say
there's a covariance matrix, a free
299
parameter.
300
So you're estimating a full covariance
matrix.
301
Now, in certain cases of these models, I'm
going to fix some off diagonal elements of
302
this covariance matrix to zero.
303
but then I want to freely estimate the
rest of this covariance matrix.
304
That becomes very difficult when you're
specifying prior distributions now because
305
we have to keep this full covariance
matrix positive definite.
306
And I have prior distributions for like an
unrestricted covariance matrix.
307
You could do a Wishard or an LKJ, say.
308
But to have this covariance matrix where
some of the entries are, say, fixed to
309
zero,
310
but I still have to keep this full
covariance matrix positive definite.
311
The prior distributions become very
challenging there.
312
And there's some workarounds that are, I
would say, allow you to estimate the
313
model, but make it difficult to describe
exactly what prior distribution did you
314
use here.
315
That's a piece that continues to challenge
me.
316
Yeah, and so what are you?
317
What I'm working on these days to try and
address that.
318
Um
319
I've been, I've looked at some ways to
decompose a covariance matrix.
320
So let's say the Kolesky factors or
things, and we have put prior
321
distributions on some decomposition of
this covariance matrix so that it's easy
322
to put, say, some normal priors on the
elements of the decomposition while
323
maintaining this positive definite full
covariance matrix.
324
And,
325
I think I made some progress there, but
then you get into this situation where I
326
want to put my prior distributions on
intuitive things.
327
If I get to like some Kolesky factor that
might have some intuitive interpretation,
328
but sometimes maybe not.
329
And you run into this problem then of,
okay, if I want to put a prior
330
distribution on this.
331
could I meaningfully do that or could a
user meaningfully do that versus they
332
would just use some default because they
don't know what else they would put on
333
that.
334
That becomes a bit of a problem too.
335
Yeah, yeah.
336
That's definitely also something I have to
handle when I am teaching these kind of
337
the compositions.
338
Like usually the way I...
339
teach that is when you do that in a linear
regression, for instance, and you would
340
try and infer not only the intercept and
the slope, but the correlation of
341
intercept and slope.
342
And so that way, if the intercept, like if
you have a negative covariance matrix, for
343
instance, that's inferred between the
intercept and the slope.
344
That means, well, if you observe a group
and if you do that in a hierarchical
345
model, particularly, that's very useful.
346
Because that means, well, if I'm in a
group of the hierarchical model where the
347
intercepts are high, that probably means
that the slopes are low.
348
So, because we have that negative
covariation.
349
And that's interesting because that allows
the model to squeeze even more information
350
from the data and so make even more
informed and accurate predictions.
351
But of course, to do that, the challenge,
352
is that you have to infer a covariance
matrix between the intercept and the
353
slope.
354
How do you infer that covariance matrix
that usually tends to be hard and
355
computationally intensive?
356
And so that's where the decomposition of
the covariance matrix enters the round.
357
So especially the Kolesky decomposition of
the covariance matrix, that's what we
358
usually recommend doing in PMC.
359
And we have that PM .LKJKoleskykov
distribution.
360
And two parametrized that you have to give
a prior on the correlation matrix, which
361
is a bit weird.
362
But when you think about it, when people
think about it, it's like, wait, prior as
363
a distribution, understand a prior as a
distribution on a correlation matrix is
364
hard to understand.
365
But actually, when you decompose, it's not
that hard.
366
because it's mainly, well, what's the
parameter that's inside a correlation
367
matrix?
368
That's parameter that says there is a
correlation between A and B.
369
And so what is your a priori belief of
that correlation between the intercept and
370
the slope?
371
And so usually you don't want the
completely flat prior, which stays any
372
correlation is possible with the same
degree of belief.
373
So that means I really think that there is
as much possibility of that
374
of slopes and intercept to be completely
positively correlated as they have a
375
possibility to be not at all correlated.
376
I'm not sure.
377
So if you think that, then you need to use
a regularizing weighting information
378
priors as you do for any other parameters.
379
So you could think of coming up with a
prior that's a bit more bell -shaped prior
380
in a way that gives more mass to the low.
381
Yeah.
382
to smaller correlations.
383
And then that's how usually you would do
that in PMC.
384
And that's what you're basically talking
about.
385
Of course, that's more complicated and it
makes your model more complex.
386
But once you have ran that model and have
that inference, that can be extremely
387
useful and powerful for posterior
analysis.
388
So it's trade -off.
389
Yeah, yeah, definitely.
390
But that reminds me of...
391
I would say like in psychology, in
psychometrics, there's still a lot of
392
hesitance to use informative priors.
393
There's still the idea of I want to do
something objective.
394
And so I want my priors to be all flat,
which especially like you say for a
395
correlation or even for other parameters,
I'm against that.
396
Now I would like to put some...
397
information in my priors always, but that
is always a challenge because like for the
398
models I work with, users are accustomed,
like I said, to specifying this big model
399
and pressing a button and it runs and it
estimates.
400
But now you do that in a Bayesian context
with these uninformative priors.
401
Sometimes you just run into problems and
you have to think more about the priors
402
and add some information.
403
Yeah.
404
Which is, if you ask me, a blessing in
disguise, right?
405
Because just because a model seems to run
doesn't mean it is giving you sensible
406
results and unbiased results.
407
I actually love the fact that usually HMC
is really unforgiving of really bad
408
priors.
409
So of course, it's usually something we
tend to teach is, try to use priors that
410
make sense, right?
411
A priori.
412
Most of the time you have more information
than you think.
413
And if you're thinking from a betting
perspective, like let's say that any
414
decision you make with your model is
actually something that's going to cost
415
you money or give you money.
416
If you were to bet on that prior, why
wouldn't you use any information that you
417
have at your disposal?
418
Why would you throw away information if
you knew that actually you had information
419
that would help you make a more
informed...
420
bet and so bet that gives you actually
more money instead of losing money.
421
And so I find that this way of framing the
priors can actually like usually works on
422
beginners because that helps them see the
like the idea.
423
It's like the idea is not to fudge your
analysis, even though I can show you how
424
to fudge your analysis, but in both ways.
425
I can use priors which are going to bias
the model, but I can also use priors that
426
are going to completely
427
unbiased the model, but just make it so
variable that it's just going to answer
428
very aggressively to any data point.
429
And do you really want that?
430
I'm not sure.
431
Do you really want to make very hard
claims based on very small data?
432
I'm not sure.
433
So again, if you come back to this idea
of, imagine that you're betting.
434
Wouldn't you use all the information you
have at your disposal?
435
That's all.
436
That's everything you're doing.
437
That doesn't mean that information is
golden.
438
That doesn't mean you have to be extremely
certain about the information you're
439
putting in.
440
That just means let's try to put some more
structure because that doesn't make any
441
sense if you're modeling football players.
442
That doesn't make any sense to allow them
to be able to score 20 goals in a game.
443
It doesn't ever happen.
444
Why would you let the model...
445
a low for that possibility.
446
You don't want that.
447
It's going to make your model harder to
estimate, longer, it's going to take
448
longer to estimate also.
449
And so that's just less efficient.
450
Yeah.
451
You mentioned too of HMC being
unforgiving.
452
And yeah, a lot of the software that I've
been working on, the model is run and
453
stand.
454
And from time to time, well, for some of
these structural equation models, there's
455
some...
456
Like, weekly identified parameters, or
maybe even unidentified parameters, but I
457
run into these situations where.
458
Somebody runs a Gibbs sampler and they
say, look, it just worked and it converged
459
and now I move this model over to Stan and
I'm getting these by modal posteriors or
460
such and such.
461
It's sort of like a bit of an education of
saying, well, the problem is at Stan.
462
The problem was the model all along, but
the Gibbs sampler just didn't.
463
tell you that there was a problem.
464
Yeah, exactly.
465
Exactly.
466
Yeah.
467
Yeah.
468
That's like, that's a joke.
469
I have actually a sticker like that, which
is a, which is a meme of, you know, that
470
meme of that, that, that guy from a, I
think it's from the notebook, right?
471
Who, who is crying and yeah, basically the
sticker I have is when someone tells me
472
that the model he has divergences in HMC.
473
So they are switching to the Metropolis
sampler and.
474
I just dance like, yeah, sure.
475
You're not going to have divergences with
the metropolis sampler.
476
Doesn't mean the model is converting as
you want.
477
And yeah, so that's really that thing
where, yeah, actually, you had problems
478
with the model already.
479
It's just that you were using a crude
instrument that wasn't able to give you
480
these diagnostics.
481
It's like doing an MRI with a stethoscope.
482
Yeah.
483
Yeah, that's not going to work.
484
It's going to look like you don't have any
problems, but maybe you do.
485
It's just like you're not using the right
tool.
486
So yeah.
487
And also this idea of, well, let's use
flat priors and just let the data speak.
488
That can work from time to time.
489
And that's definitely going to be the case
anyways, if you have a lot of data.
490
Even if you're using weekly regularizing
priors, that's exactly the goal.
491
It's just to give you enough structure to
the model in case the data are not
492
informative for some parameters.
493
The bigger the model, the more parameters,
well, the less informed the parameters are
494
going to be if your data stay what they
are, keep being what they are, right?
495
If you don't have more.
496
And also that assumes that the data are
perfect, that there's no bias, that the
497
data are completely trustworthy.
498
Do you actually believe that?
499
If you don't, well, then...
500
You already know something about your
data, right?
501
That's your prior right here.
502
If you think that there is sampling bias
and you kind of know why, well, that's a
503
prior information.
504
So why wouldn't you tell that in the
model?
505
Again, from that betting perspective,
you're just making your model's life
506
harder and your inference is potentially
wrong.
507
I'm guessing that's not what you want as
the modeler.
508
Yeah, you can trust the data blindly.
509
Should you though?
510
That's a question you have to answer each
time you're doing a model.
511
Yep.
512
Most often than not, you cannot.
513
Yeah, yeah.
514
Yeah, the HMC failing thing, I think
that's a place where you can really see
515
the progress that's been made in Bayesian
estimation.
516
Just like say in the 20 some years that
I've been doing it, I can think back to
517
starting out with wind bugs.
518
You're just happy to get the thing to run.
519
and to give you some decent convergence
diagnostics.
520
I think a lot of the things we did around
the start of wind bugs, if you try to run
521
them in Stan now, you find there were a
lot of problems that were just hidden or
522
you're kind of overlooked.
523
Yeah, yeah, yeah, for sure.
524
And definitely that I think we've hammered
that point in the community quite a lot.
525
in the last few years.
526
And so definitely those points that I've
been making in the last few minutes are
527
clearly starting to percolate.
528
And I think the situation is way better
than it was a few years ago, just to be
529
clear and not come across as complaining
statisticians.
530
Because I'm already French.
531
So people already imagine that I'm going
to assume that I'm going to complain.
532
So if on top of that, I complain about
stats, I'm done.
533
People are not going to listen to the
podcast anymore.
534
I think you'll be all right.
535
So to continue, I'd like to talk about
your Blavin package and what inspired the
536
development of this package and how does
it enhance the capabilities of researchers
537
in doing BSEM?
538
Yeah, I think I said earlier my...
539
PhD was about some Bayesian factor
analysis models and looking at some
540
missing data issues.
541
I would say it wasn't the greatest PhD
thesis, but it was finished.
542
And at the time, I thought it would be
nice to have some software that would give
543
you some somewhat simple way to specify a
model.
544
And then it could be translated to
545
like at the time wind bugs so that you
could have some easier MCMC estimation.
546
But at that time, like, I, the, like R
wasn't as quite as developed and my skills
547
weren't quite there to be able to do that
all on my own.
548
So I left it for a few years, then around
2009 or so, I think.
549
Some R packages for frequent structural
equation models were becoming better
550
developed and more supported.
551
So a few years later, I met the developer
of the LaVon package, which does frequent
552
structural equation models and did some
work with him.
553
And from there I thought, well,
554
he's done some of the hard work already
just with model specification and setting
555
up the model likelihood.
556
So I built this package on top of what was
already there to do like the Bayesian
557
version of that model estimation.
558
And then it has just gone from there.
559
I think I continue to learn more things
about these models or encounter tricky
560
issues that I wasn't quite aware of when I
started.
561
And I just have...
562
continue it on.
563
Yeah.
564
Well, that sounds like a fun project for
sure.
565
And how would people use it right now?
566
When would you recommend using your
package for which type of problems?
567
Well, the idea from the start was
always...
568
make the model specification and
everything very similar to the LaVon
569
package for Frequence models because that
package was already fairly popular among
570
people that use these models.
571
And the idea was, well, they could move to
doing a Bayesian version without having to
572
learn a brand new model specification.
573
They could already do something similar to
what they had been doing on the Frequence
574
side.
575
So that's like,
576
from the start where we, the idea that we
had or what we wanted to do with a package
577
and then who would use it?
578
I think it could be for some of these
measurement problems, like I said, with
579
item response modelers or things if they
wanted to do a Bayesian version of some of
580
these models that's currently possible and
blah, blah, and another place is.
581
With something kind of similar to the
DAGs, the directed acyclic graphs we talk
582
about, especially in the social sciences,
people have these theories about they have
583
a collection of variables and what
variables cause what other variables and
584
they want to estimate some regression type
relationships between these things.
585
You would see it often like an
observational data where you can't really
586
do these.
587
these manipulations the way you could in
an experiment.
588
But the idea is that you could specify a
graph like that and use Blofond to try to
589
estimate these regression -like
relationships that if the graph is
590
correct, you might interpret it as causal
relationships.
591
Yeah, fascinating, fascinating.
592
I love that.
593
And I'll put the package, of course, in
the show notes.
594
And I encourage people to take a look at
the website.
595
There are some tutorials and packages of
the, sorry, some tutorials on how to use
596
the package on there.
597
So yeah, definitely take a look at the
resources that are on the website.
598
And of course, everything is on the show
notes.
599
Another topic I thought was very
interesting from your background is that
600
your research also touches on forecasting
and subjective probability.
601
Can you discuss how Bayesian methods
improve these processes, particularly in
602
crowdsourcing wisdom, which is something
you've worked on quite a lot?
603
Yeah, I started working on that.
604
It was probably 2009 or 2010.
605
So at that time, I think...
606
Tools like Mechanical Turk were becoming
more usable and so people were looking at
607
this wisdom of Krausen saying, can we
recruit a large group of people from the
608
internet?
609
And if we average their predictions, do
those make for good predictions?
610
I got involved in some of that work,
especially through some forecasting
611
tournaments that were being run by
612
the US government or some branches of the
US government at the time.
613
I think Bayesian tools there first made
some model estimations easier just the way
614
they sometimes do in general.
615
But also with forecasting, it's all about
uncertainty.
616
You might say, here's what I think will
happen.
617
But then you also want to have some
characterization of.
618
your certainty or uncertainty that
something happens.
619
I think that's where the Bayesian approach
was really helpful.
620
Of course, you always have this trade -off
with you are giving a forecast often to
621
like a decision maker or an executive or
someone that is a leader.
622
Those people sometimes want the simplest
forecast possible and it's sometimes
623
difficult to convince them that,
624
Well, you also want to look at the
uncertainty around this forecast as
625
opposed to just a point estimate.
626
Yeah.
627
But that's some of the ways we were using
Bayesian methods, at least to try to
628
characterize uncertainty.
629
Yeah.
630
Yeah.
631
I'm becoming more and more authoritative
on these fronts, you know, just not even
632
giving the point estimates anymore and by
default giving a range for the
633
predictions.
634
and then people have to ask you for the
point estimates.
635
Then I can make the point of, do you
really want that?
636
Why do you want that one?
637
And why do you want the mean more than the
tail?
638
Maybe in your case, actually, the tail
scenarios are more interesting.
639
So keep that in mind.
640
So yeah, people have to opt in to get the
point estimates.
641
And well, the human brain being what it
is, usually it's happy with the default.
642
And so...
643
Making the default better is something I'm
trying to actually actively do.
644
That's a good point.
645
So what for reporting modeling results,
you avoid posterior means.
646
All you give them is like a posterior
interval or something.
647
A range.
648
Yeah.
649
Yeah.
650
Yeah, exactly.
651
Not putting particular emphasis on the
mean.
652
Because otherwise what's going to end up
happening, and that's extremely
653
frustrating to me, is...
654
I mentioned that you're comparing two
options.
655
And so you have the posterior on option A,
the posterior on option B.
656
You're looking at the first plot of A and
B.
657
They seem to overlap.
658
So then you compute the difference of the
posteriors.
659
So B minus A.
660
And you're seeing where it spans on the
real line.
661
And if option A and B are close enough,
662
the HDI, so the highest density interval,
is going to overlap with zero.
663
And it seems like zero is a magic number
that makes the whole HDI collapse on one
664
point.
665
So basically, the zero is a black hole
which just sucks everything onto itself,
666
and then the whole range is zero.
667
And then people are just going to say, oh,
but that's weird because, no, I think
668
there is some difference between A and B.
669
And then you have to say, but that's not
what the model is saying.
670
You're just looking at zero and you see
that the HDI overlaps zero at some point.
671
But actually the model is saying that, I
don't know, there is an 86 % chance that
672
option A is actually better than option B
is actually better than A.
673
So, you know, there is a five in six
chance, which is absolutely non -next
674
level that B is indeed better than A, but
we can actually rule out the possibility
675
that A is better than B.
676
That's what the model is saying.
677
It's not telling you that there is no
difference.
678
And it's not telling you that
679
A is definitely better than B.
680
And that is still in it.
681
I'm trying to crack.
682
But yeah, here you cannot make the zero
disappear, right?
683
But the only thing you can do is make sure
that people don't interpret the zero as a
684
black hole.
685
That's the main thing.
686
Yeah, yeah.
687
Yeah, yeah, that's a good point.
688
I can see that being challenging for
people that come from frequentist models
689
because what they're accustomed to, the
maximum likelihood estimate.
690
And it's all about those point estimates.
691
But I like the idea of not even supplying
those point estimates.
692
Yeah.
693
Yeah, yeah.
694
I mean, and that makes sense in the way
that's just a distraction.
695
It doesn't mean anything in particular.
696
That's mainly a distraction.
697
What's more important here is the range.
698
of the estimates.
699
So, you know, like give the range and give
the point estimates if people ask for it.
700
But otherwise, that's more distraction
than anything else.
701
And I think I got that idea from listening
to a talk by Richard MacGarriff, who was
702
talking about something he called table
two fallacy.
703
Yeah, I know that.
704
Where usually the present the table of
estimates in the table two.
705
And usually people tend to, his point with
that, people tend to interpret the
706
coefficient on a linear regression, for
instance, as all of them as causal, but
707
they are not.
708
The only parameter that's really causally
interpretable is the one that relates the
709
treatment to the outcome.
710
The other one, for instance, from a
mediator to the outcome, or...
711
the one from a confounder to the outcome,
you cannot interpret that parameter as
712
causal.
713
Or you have to do the causal graph
analysis and then see if the linear
714
regression you ran actually corresponds to
the one you would have to run in this new
715
causal DAG to identify or the direct or
the total causal effect of that new
716
variable that you're taking as the
treatment.
717
basically you're changing the treatment
here.
718
So you have to change the model
potentially.
719
And so you cannot interpret and should
absolutely not interpret the parameters
720
that are not the one from the treatment to
the outcome as causally interpretable.
721
And so to avoid that fallacy, he was
suggesting two options or you actually
722
provide the interpretation of that
parameter in the current DAG that you
723
have.
724
And say, if it's not causally
interpretable in that case, which DAG you
725
would have, which regression, sorry, which
model would have to use, which is
726
different from the one you actually have
RAM to actually be able to interpret that
727
coefficient causally.
728
Or you just don't report these parameters,
these coefficients, because they are not
729
the point of the analysis.
730
The point of the analysis is to relate the
treatment to the outcome and see what the
731
effect of the treatment is on the outcome.
732
not what the treatment of a camp founder
on the outcome is.
733
So why would you report that in the first
place?
734
You can report it if people ask for it,
but you don't, you should not report it by
735
default.
736
Yeah, yeah.
737
There's some good like tie -ins to
structural equation models there too,
738
because I think like in some of those,
some of McElroy's examples, he dabbles a
739
little bit in structural equation model
and to, it's kind of like a one possible
740
solution here to,
741
to really saying what could we interpret
causally or not in the presence of
742
confounding variables or like there's the
colliders that also cause problems if you
743
include them in a regression.
744
Yeah, he does a little bit.
745
I've seen some of his examples like what
structural equation model source of
746
things.
747
I think there's something interesting
there about informing what predictors
748
should go in a regression or.
749
what could we interpret causally out of a
particular model?
750
Yeah, exactly.
751
And I have actually linked to the table 2
fallacy thing I was talking about, his
752
video of that.
753
So this will be in the show notes for
people who want to dig deeper.
754
Yes.
755
And, yeah, so we're in this discussion.
756
I really love to talk about these topics,
as you can see, and I've really deeply
757
enjoyed diving deeper into them.
758
And still, I'm diving deeper into these
topics for 2024.
759
That's one of my objectives, so that's
really fun.
760
Yeah.
761
Maybe let's talk about latent viable
models, because you also work on that.
762
And if I understood correctly, they are
quite crucial in psychology.
763
So how do you approach these models,
especially in the context of patient
764
stance?
765
And maybe explain, also give us a primer
on what latent viable models are.
766
Yeah, I would.
767
So sometimes I almost use them as like
just another term for structural equation
768
model.
769
They're very related.
770
I would say.
771
I would say if I'm around psychology or
psychometrics people, I would use the term
772
structural equation model.
773
But if I'm around statistics people, I
might more often use the term latent
774
variable model because I think that term
latent variable, or maybe sometimes people
775
might say a hidden variable or something
that's unobserved.
776
But it's like in...
777
in structural equation modeling, that is
sort of just like a random effect or a
778
random parameter that we assume has some
influence on other observed variables.
779
And that you can never observe it.
780
That's right.
781
And so the traditional example is...
782
maybe something related to intelligence or
say like a person's math aptitude,
783
something you would use a standardized
test for.
784
You can't directly observe it.
785
You can ask many questions that get at a
person's math aptitude.
786
And we could assume, yes, there's this
latent aptitude that each person has that
787
we are trying to measure with all of our
questions on a standardized test.
788
That sort of gets at the idea of latent
variable.
789
Yeah.
790
Yeah.
791
And like, or another example would be the
latent popularity of political parties.
792
Like, you never really observed them.
793
Actually, you just have an idea with
polls.
794
You had a better idea with elections, but
even elections are not a perfect image of
795
that because nobody, like, not everybody
goes and vote.
796
So that's thank you again.
797
actually never observe the actual
popularity of political parties in the
798
total population because, well, even
elections don't make a perfect job of
799
that.
800
Yeah, yeah, yeah.
801
Yeah, and then people will get into a lot
of deep philosophy conversations about
802
does this latent variable even exist and
how could one characterize that?
803
And
804
Personally, I don't often get into those
deep philosophy conversations.
805
I just more think of this as a model than
within this model.
806
It could be a random parameter.
807
And I guess maybe it's just my personal
bias.
808
I don't think about it too abstractly.
809
I just think about how does this latent
variable function in a model and how can I
810
fit this model to data?
811
Yeah, I see.
812
And so in these cases, how do you found
that using a basin framework has been
813
helpful?
814
Yeah, I think related to it, I was
discussing before about these latent
815
variables are often like random effects.
816
And so from a Bayesian point of view, you
can sample those parameters and look at
817
how their uncertainty filters through to
other parts of your model.
818
That's all.
819
very straightforward from a Bayesian point
of view.
820
I think those are some of the big
advantages.
821
OK, I see.
822
I see.
823
Yeah.
824
If we de -zoom a bit, I'm actually
curious, what would you say is the biggest
825
hurdle in the Bayesian workflow currently?
826
Um
827
There's always challenges with how long
does it take MCMC to run, especially for
828
people coming from frequentist models or
things where, for some frequentist models,
829
especially with these structural equation
or latent variable models, you can get
830
some maximum likelihood estimates in a
couple of seconds.
831
And there's cases with MCMC, it might take
much longer depending on how the model was
832
set up or how tailored.
833
your estimation strategy is to a
particular model.
834
So I think speed is always an issue.
835
And that I think could maybe detract some
people from doing Bayesian modeling
836
sometimes.
837
I would say maybe the other barrier to the
workflow is just getting people to slow
838
down and just be happy with slowing down
with working through their model.
839
I think especially in the social sciences
where I work, people become too accustomed
840
to specifying their model, pressing a
button, getting the results immediately
841
and writing it and being done.
842
And I think that's not how good Bayesian
modeling happens.
843
Good Bayesian modeling, you sit back a
little bit and think through everything.
844
And...
845
I think is a challenge convincing people
sometimes to make that a habitual part of
846
the workflow.
847
Yeah.
848
Bayesian models need love.
849
You need to give it love for sure.
850
I personally have been working lately on
an academic project like that where we're
851
writing a paper on, basically it's a trade
paper on biology, marine biology trade.
852
And the model is extremely complex.
853
And that's why I'm on this project is to
work with the academics working on it who
854
are extremely knowledgeable, of course,
but on their domain.
855
And me, I don't understand anything about
the biology part, but I'm just here to try
856
and make the model work.
857
And the one is tremendously complicated
because the phenomenon they are studying
858
is extremely complex.
859
So.
860
Yeah, but like here, the amazing thing is
that the person leading the project, Aaron
861
McNeil, has a huge appetite for that kind
of work, right?
862
And really love doing the Bayesian model,
coding it, and then improving it together.
863
But definitely that's a big endeavor,
takes a lot of time.
864
But then the model is extremely powerful
afterwards and you can get a lot of
865
inferences that you cannot have with a
classic trivial model.
866
So, you know, there is no free lunch,
right?
867
If your model is trivial, your inferences
probably will be, unless you're extremely
868
lucky and you're just working on something
that nobody has worked on before.
869
So then it's like, just a forest
completely new.
870
But otherwise, if you want interesting
inferences, you have to have an
871
interesting model.
872
And that takes time, takes dedication, but
for sure it's extremely...
873
interesting and then after once it gives
you a lot of power.
874
So, you know, it's a bit of a...
875
That's also a bit frustrating to me in the
sense that the model is actually not going
876
to be really part of the paper, right?
877
People just care about the results of the
model.
878
But me, it's like, and I mean, it makes
sense, right?
879
It's like when you buy a car, yeah, the
engine is important, but you care about
880
the whole car, right?
881
But I'm guessing that the person who built
the engine is like, yeah, but without the
882
engine, it's not even a car.
883
So why don't you give credit to the
engine?
884
But that makes sense.
885
But it was really fun for me to see
because for me, the model is really the
886
thing.
887
But it's actually almost not even going to
be a part of the paper.
888
It's going to be an annex or something
like that.
889
Yeah.
890
That's really weird.
891
Put it in the appendix.
892
Yeah.
893
Yeah.
894
So I've already taken a lot of your time,
Ed.
895
So let's head up for the last two
questions.
896
Before that, though, I'm curious, looking
forward, what exciting developments do you
897
foresee in patient psychometrics?
898
Uh, the one that I see coming is related
to the speed issue again.
899
So, um, I, what there's, there's more and
more MCMC stuff with GPUs.
900
And I was at a stand meeting last year
where they're talking about, um, you know,
901
imagine being able to run hundreds of
parallel chains that all like share a burn
902
in so that, you know,
903
one chain isn't going to go off and do
something really crazy.
904
I think all of that is really interesting.
905
And I think that could really improve some
of these bigger psychometric models that
906
can take a while to run if we could do
lots of parallel chains and be pretty sure
907
that they're gonna converge.
908
I think is something coming that will be
very useful.
909
Yeah, that definitely sounds like an
awesome project.
910
So before letting you go, Ed, I'm going to
ask you the last two questions I ask every
911
guest at the end of the show.
912
First one, if you had unlimited time and
resources, which problem would you try to
913
solve?
914
Yes.
915
So I guess people should say, you know,
world hunger or world peace or something,
916
but I think I would probably go for
something that's closer to what I do.
917
And one thing that comes to mind involves
maybe improving math education or making
918
it more accessible to more people.
919
I think at least in the US, like for
younger kids growing up with math, it
920
feels a little bit like sports where if
you are fortunate to have gotten into it
921
really early, then you like have this
advantage and you do well.
922
But if you come into math late, say maybe
as a teenager, I think what happens
923
sometimes is,
924
You see other people that are way ahead of
you, like solving problems you have no
925
idea how to do.
926
And then you get maybe not so enthusiastic
and you just leave and do something else
927
with your life.
928
I think more could be done just to try to
get more interested people like staying in
929
math related fields and doing more work
there.
930
I think.
931
with unlimited resources, that's the sort
of thing that I would try to do.
932
Yeah, I love that.
933
And definitely I can, yeah, I can
understand why you would say that.
934
That's a very good point.
935
As I was to say, I was late coming around
to math myself.
936
I think I don't know what happens in every
country, but in the US, it feels like...
937
You're just expected to think that math is
this tough thing that's not for you.
938
And unless you have like influences in
your life that would convince you
939
otherwise, I think a lot of kids just
don't even make an attempt to do something
940
with math.
941
Yeah, yeah, that's a good point.
942
And second question, if you could have
dinner with any great scientific mind,
943
dead, alive, or fictional, who would it
be?
944
Yeah, this is one that is easy to
overthink or to really make a big thing
945
about.
946
But so here's one thing that I think
about.
947
There's, I think it's called Stigler's law
about it's related to this idea that the
948
person who is known for like a major
finding or scientific result often isn't
949
the one that did the hard work.
950
Maybe they were the ones that that were
like promoted themselves the most or or
951
otherwise just got their name attached and
so If I'm having dinner, I want it to be
952
more of a low -key dinner.
953
So I don't necessarily want to go for the
most famous person that is the most known
954
for something because I worry that they
would just like promote themselves the
955
whole time or you would feel like you're
talking to a robot because they're
956
They're like, they see themselves as kind
of above everyone.
957
So with that in mind, and keeping it on
the Bayesian viewpoint, one person that
958
comes to mind is Arianna Rosenbluth, who
was one of the, I think was the first to
959
like program a Metropolis Hastings
algorithm and did it in the context of the
960
Manhattan project during World War II.
961
So I think she would be an interesting
person to have dinner with.
962
She clearly did some important work.
963
Didn't quite get the recognition that some
others did, but also I think she didn't
964
have a traditional academic career.
965
So that means that dinner, you know, you
could talk about some work things, but
966
also I think she would be interesting to
talk to just, you know, just about other
967
non -work things.
968
That's the kind of dinner that I would
like to have.
969
So that's my answer.
970
Love it.
971
Love it, Ed.
972
Fantastic answer.
973
And definitely invite me to that dinner.
974
That would be fascinating.
975
Fantastic.
976
Thanks a lot, Ed.
977
We can call it a show.
978
That was great.
979
I learned a lot.
980
And as usual, I will put a link to your
website and your socials and tutorials.
981
in the show notes for those who want to
dig deeper.
982
Thank you again.
983
All right.
984
Thanks for taking the time and being on
the show.
985
Thanks for having me.
986
It was fun.
987
This has been another episode of Learning
Bayesian Statistics.
988
Be sure to rate, review, and follow the
show on your favorite podcatcher, and
989
visit learnbaystats .com for more
resources about today's topics, as well as
990
access to more episodes to help you reach
true Bayesian state of mind.
991
That's learnbaystats .com.
992
Our theme music is Good Bayesian by Baba
Brinkman, fit MC Lass and Meghiraam.
993
Check out his awesome work at bababrinkman
.com.
994
I'm your host.
995
Alex and Dora.
996
You can follow me on Twitter at Alex
underscore and Dora like the country.
997
You can support the show and unlock
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998
.com slash LearnBasedDance.
999
Thank you so much for listening and for
your support.
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