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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

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993

Check out his awesome work at bababrinkman

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994

I'm your host.

995

Alex and Dora.

996

You can follow me on Twitter at Alex

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997

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998

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999

Thank you so much for listening and for

your support.

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