Proudly sponsored by PyMC Labs, the Bayesian Consultancy. Book a call, or get in touch!
Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work !
Visit our Patreon page to unlock exclusive Bayesian swag 😉
Takeaways
- Bayesian methods align better with researchers’ intuitive understanding of research questions and provide more tools to evaluate and understand models.
- Prior sensitivity analysis is crucial for understanding the robustness of findings to changes in priors and helps in contextualizing research findings.
- Bayesian methods offer an elegant and efficient way to handle missing data in longitudinal studies, providing more flexibility and information for researchers.
- Fit indices in Bayesian model selection are effective in detecting underfitting but may struggle to detect overfitting, highlighting the need for caution in model complexity.
- Bayesian methods have the potential to revolutionize educational research by addressing the challenges of small samples, complex nesting structures, and longitudinal data.
- Posterior predictive checks are valuable for model evaluation and selection.
Chapters
00:00 The Power and Importance of Priors
09:29 Updating Beliefs and Choosing Reasonable Priors
16:08 Assessing Robustness with Prior Sensitivity Analysis
34:53 Aligning Bayesian Methods with Researchers’ Thinking
37:10 Detecting Overfitting in SEM
43:48 Evaluating Model Fit with Posterior Predictive Checks
47:44 Teaching Bayesian Methods
54:07 Future Developments in Bayesian Statistics
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, Julio, Edvin Saveljev, Frederick Ayala, Jeffrey Powell, Gal Kampel, Adan Romero, Will Geary, Blake Walters, Jonathan Morgan and Francesco Madrisotti.
Links from the show
- Sonja’s website: https://winterstat.github.io/
- Sonja on Twitter: https://twitter.com/winterstat
- Sonja on GitHub: https://github.com/winterstat
- Under-Fitting and Over-Fitting – The Performance of Bayesian Model Selection and Fit Indices in SEM: https://www.tandfonline.com/doi/full/10.1080/10705511.2023.2280952
- LBS #102 – Bayesian Structural Equation Modeling & Causal Inference in Psychometrics, with Ed Merkle: https://youtu.be/lXd-qstzTh4?si=jLg_qZTt1oQqRO0R
- LBS #107 – Amortized Bayesian Inference with Deep Neural Networks, with Marvin Schmitt: https://learnbayesstats.com/episode/107-amortized-bayesian-inference-deep-neural-networks-marvin-schmitt/
- BayesFlow tutorial: https://bayesflow.org/_examples/Intro_Amortized_Posterior_Estimation.html
- LBS #106 Active Statistics, Two Truths & a Lie, with Andrew Gelman: https://learnbayesstats.com/episode/106-active-statistics-two-truths-a-lie-andrew-gelman/
- LBS #61 Why we still use non-Bayesian methods, with EJ Wagenmakers: https://learnbayesstats.com/episode/61-why-we-still-use-non-bayesian-methods-ej-wagenmakers/
- Bayesian Workflow paper: https://arxiv.org/abs/2011.01808
- Michael Betancourts’blog: https://betanalpha.github.io/writing/
- LBS #35 The Past, Present & Future of BRMS, with Paul Bürkner: https://learnbayesstats.com/episode/35-past-present-future-brms-paul-burkner/
- Bayesian Model-Building Interface in Python: https://bambinos.github.io/bambi/
- Advanced Regression online course: https://www.intuitivebayes.com/advanced-regression
- BLIMP: https://www.appliedmissingdata.com/blimp
Transcript
This is an automatic transcript and may therefore contain errors. Please get in touch if you’re willing to correct them.
Transcript
Priors represent a crucial part of the
Bayesian workflow, and actually a big
2
reason for its power and usefulness.
3
But why is that?
4
How do you choose reasonable priors in
your models?
5
What even is a reasonable prior?
6
These are deep questions that today's
guest, Sonja Winter, will guide us
7
through.
8
an assistant professor in the College of
Education and Human Development of the
9
University of Missouri, Sonia's research
focuses on the development and application
10
of patient approaches to the analysis of
educational and developmental
11
psychological data, with a specific
emphasis on the role of priors.
12
What a coincidence!
13
In this episode, she shares insights on
the selection of priors, prior sensitivity
14
analysis, and the challenges of working
15
with longitudinal data.
16
She also explores the implications of
Bayesian methods for model selection and
17
fit indices in structural equation
modeling, as well as the challenges of
18
detecting overfitting in models.
19
When she's not working, you'll find Sonja
baking delicious treats, gardening, or
20
watching beautiful birds.
21
This is Learning Bayesian Statistics,
episode.
22
Welcome to Learning Bayesian Statistics, a
podcast about Bayesian inference, the
23
methods, the projects, and the people who
make it possible.
24
I'm your host, Alex Andorra.
25
You can follow me on Twitter at alex
.andorra, like the country.
26
For any info about the show, learnbasedats
.com is Laplace to be.
27
Show notes, becoming a corporate sponsor,
unlocking Bayesian Merge, supporting the
28
show on Patreon, everything is in there.
29
That's learnbasedats .com.
30
If you're interested in one -on -one
mentorship, online courses, or statistical
31
consulting, feel free to reach out and
book a call.
32
at topmate .io slash alex underscore and
dora see you around folks and best patient
33
wishes to you all.
34
Hello my dear patients, today I want to
thank the fantastic Jonathan Morgan and
35
Francesco Madrisotti for supporting the
show on Patreon.
36
Your support is invaluable and literally
makes this show possible.
37
can't wait to talk with you guys in the
Slack channel.
38
Second, with my friends and fellow PymC
core developers, Ravin Kumar and Tommy
39
Capretto, we've just released our new
online course, Advanced Regression with
40
Bambi and PymC.
41
And honestly, after two years of
development, it feels really great to get
42
these out into the world, not only because
it was, well, long and intense, but mainly
43
because I am so proud of the level of
44
of details, teachings, and exercises that
we've packed into this one.
45
It's basically the course I wish I had
once I had gone through the beginner's
46
phase when learning patience tests, that
moment when you're like...
47
Okay, I know how to do basic models, but
where do I go from here?
48
I remember feeling quite lost, so we
wanted to give you a one -stop shop for
49
such intermediate models with the most
content possible, as evergreen as it gets.
50
If that sounds interesting, go to
intuitivebase .com and check out the full
51
syllabus.
52
We're enrolling the first cohort as we
speak!
53
Of course, you get a 10 % discount if
you're a patron of the show.
54
Go to the Patreon page or the Slack
channel to get the code.
55
Okay, back to the show now and looking
forward to seeing you in the intuitive
56
base discourse.
57
Sonia Winter, welcome to Learning Bayesian
Statistics.
58
Thank you.
59
Thanks for having me.
60
I'm really excited to talk to you today.
61
Same, same.
62
That's a treat.
63
I have a lot of questions.
64
I really love.
65
like everything you're doing in your
research.
66
We're going to talk a lot about priors
today, folks.
67
So yeah, like get ready.
68
But first, can you provide a brief
overview of your research interests and
69
how patient methods play a role in your
work?
70
Yeah, sure.
71
So my background is actually in
developmental psychology.
72
I did a bachelor or master's degree at
Utrecht University.
73
And during that time, I really realized
that a lot of work needed to be done on
74
the analysis part of social science
research.
75
And so I switched and got really into
structural equation models, which are
76
these big multivariate models that include
latent variables.
77
I'm sure we'll talk more about that later.
78
But those models can be hard to estimate
and there are all these issues.
79
And so I was introduced to Bayesian
statistics.
80
right after my master's degree when I was
working with Rens van der Schoot, also at
81
Utrecht University.
82
And he asked me to do this big literature
review about it with him.
83
And that really introduced me.
84
And so now I focus a lot on Bayesian
estimation and how it can help us estimate
85
these structural equation models.
86
And then specifically more recently, I've
really been focusing on how those priors
87
can really help us.
88
both with estimation and also just with
understanding our models a little bit
89
better.
90
So yeah, I'm really excited about all of
that.
91
Yeah, I can guess that sounds awesome.
92
So structural equation modeling, we
already talked about it on the show.
93
So today we're going to focus a bit more
on priors and how that fits into the SEM
94
framework.
95
So for people who don't know about SEM, I
definitely recommend episode 102 with Ed
96
Merkel.
97
And we talked exactly about structural
equation modeling and causal inference in
98
psychometrics.
99
So that will be a.
100
a very good introduction i think to these
topics for people and what i'm curious
101
about sonia is you work a lot on priors
and things like that but how how did you
102
end up working on that was something that
you were always curious about or that
103
something that appeared later later on in
your in your phd studies
104
I would say definitely something that
started or piqued my interest a little bit
105
later.
106
I think so after I first got familiarized
with Bayesian methods, I was excited
107
mostly by how it could help, like priors
could help us estimate, like avoid
108
negative variances and those types of
things.
109
But I saw them more as a pragmatic tool to
help with that.
110
And I didn't really focus so much on that.
111
I feel like I also was a little bit afraid
at the time of, you know, those
112
researchers who talk a lot about, well, we
shouldn't really make our priors
113
informative because that's subjective and
that's bad.
114
And so I really typically use like
uninformative priors or like software
115
defaults for a lot of my work in the
beginning.
116
But then during my PhD studies, I
actually.
117
Well, first of all, I worked with another
researcher, Sanaa Smith, who was also a
118
PhD student at the time.
119
And she was really intrigued by something
she found that these software defaults can
120
really cause issues when you're,
especially when your data is like very
121
small, it can, it can make your results
look wild.
122
And so we worked on this paper together
and created a shiny app to demonstrate all
123
of that.
124
And that made me realize that maybe
uninformative priors.
125
are not always the best way to go.
126
And also a prior that looks informative in
one scenario might be relatively
127
uninformative in another.
128
And so I really started shifting my, my
perspective on priors and focusing more on
129
how ignoring them is kind of like ignoring
the best part of Bayesian in my opinion,
130
at this point.
131
and so now I really want to look at how,
how they can help us and how we can be
132
thoughtful.
133
We don't want to drive our science by
priors, right?
134
We want to learn something new from our
data, but we find that balance is really
135
what I'm looking for now.
136
Yeah, well, what a fantastic application
of updating your belief, right?
137
From a meta standpoint, you just like
updated your priors pretty aggressively
138
and also very rationally.
139
That's really impressive.
140
Well done.
141
Because that's hard to do also.
142
It's not something we like to do.
143
So that's great.
144
Well done on doing that.
145
And actually now that you're on the other
side, how do you approach the selection of
146
priors in your research and what advice do
you have for people new to Bayesian
147
methods?
148
Yeah, great question.
149
I think at least within structural
equation modeling, we as like applied
150
researchers are helped somewhat because
distributions, at least for priors, are
151
sort of clear.
152
Like you don't have to think too much
about them.
153
And so you can immediately jump into
thinking about, okay, what level of
154
information do I want to convey in those
priors?
155
And I think whenever I'm working with
applied researchers, I try to strike a
156
balance with them because I know they are
not typically comfortable using like super
157
informative priors that are really narrow.
158
And so I just asked them to think about,
well, what would be a reasonable range?
159
Like if we are estimating a linear
regression parameter, what would that
160
effect size look like?
161
Right.
162
It might be zero or it might be two, but
it's probably not going to be 20.
163
And so we can.
164
sort of shape our prior to align with
those sort of expectations about how
165
probable certain values are versus others.
166
It's a really, I don't know, interactive
process between me and the researcher to
167
get this right, especially for those types
of parameters that they are really
168
interested in.
169
I think another type of parameter that is
more challenging for applied researchers
170
are those that are placed on residual
variances, for example.
171
Like people typically don't...
172
think about the part of the outcome that
they can't explain that much.
173
And so that's where I do rely a bit more
on sort of, I don't know, industry
174
standard choices that are typically not
super informative.
175
But then once we pick our like target
priors, I always advise the researcher to
176
follow it up with a sensitivity analysis
to see.
177
like how robust their findings are to
changes in those priorities, either making
178
them more informative or less informative.
179
And so yeah, that's really the approach I
take.
180
Of course, if someone wants to go full
base and full informative and they have
181
this, this wealth of previous research to
draw from, then I'm all for going, going
182
that route as well.
183
It's just not as common.
184
Hmm.
185
Hmm.
186
Yeah, I see.
187
in what, what are the...
188
main difficulties you see from people that
you advise like that?
189
Where do you see them having more defenses
up or just more difficulties because they
190
have a hard time wrapping their head
around a specific concept?
191
I think just all over, I think if anyone
has ever tried to do like a power analysis
192
working with researchers, it's sort of a
similar concept because
193
It is not, at least in my field or the
people I work with are not very typically
194
already thinking about the exact parameter
estimates that they are expecting to see,
195
right?
196
They are just, they just go with the
hypothesis.
197
I think these two things are correlated
and they might not even go as far as to
198
think, is it positive or negative?
199
So then once you ask them those questions,
it really forces them to go much deeper on
200
their theory and really consider like.
201
What is, what am I expecting?
202
What is reasonable based on what I know
from, from previous studies or just
203
experience.
204
And that can be kind of challenging.
205
It's, it's kind of, I think sometimes the
researchers might feel like I'm
206
criticizing them for not knowing, but I
think that's perfectly normal to not know.
207
Like we already have so many other things
to think about.
208
But it definitely.
209
is kind of a hurdle.
210
Also the time commitment, I think, to
really consider the priors, especially if
211
you're coming from a frequentist realm
where you just say, okay, maximum
212
likelihood go.
213
Not only do you not have to think about
the estimation, but then also your results
214
are almost instant.
215
And so that's always kind of a challenge
as well.
216
I see.
217
Yeah.
218
Yeah.
219
Definitely something also I seen, I seen
beginners.
220
yeah, it, it really depends on also where
they are coming from, as you were saying.
221
Yeah.
222
I did.
223
Your advice will depend a lot on that.
224
yeah.
225
Yeah.
226
And actually you work also a lot on prior
sensitivity analysis.
227
can you, can you tell people what that is?
228
And the importance of it in your, in your
modeling workflow and.
229
how you incorporate it into your research.
230
Yeah.
231
So a sensitivity analysis for priors is
something that you typically do after you
232
run your main analysis.
233
So you come up with your target set of
priors for all your parameters, estimate
234
the model, look at the results, look at
the posteriors.
235
And then in the next step, you think
about, well, how can I change these
236
priors?
237
in sort of meaningful ways, either making
them more informative, perhaps making them
238
represent some other theory, making them
less informative as well.
239
So making the influence of the prior
weaker in your results.
240
And then you rerun your analysis for all
of those different prior scenarios, and
241
then compare those results to the ones
that you actually obtained with your
242
target analysis and your target priors.
243
And the idea here is to see,
244
how much your results actually depend on
those prior beliefs that you came into the
245
analysis with.
246
If you don't find any differences, then
you can say, well, my results are mostly
247
influenced by my data, by the new evidence
that I obtained.
248
They are robust to changes in prior
beliefs, right?
249
It doesn't really matter what beliefs you
came into the analysis with.
250
The results are going to be the same,
which is great.
251
In other cases, you might find that your
results do change meaningfully.
252
So for example, in effect that was
significant with your priors is no longer
253
significant using a frequentist term here,
but hopefully people will understand once
254
you change your priors.
255
And that's, of course, is a little bit
more difficult to handle because what do
256
you do?
257
I want to say that the goal is not to
258
use the sensitivity analysis to then go
back and change your priors and run the
259
analysis again and report that in your
paper.
260
That would be sort of akin to p -hacking.
261
Instead, I think it just contextualizes
your findings.
262
It's showing that the knowledge you came
into the analysis with is partially
263
driving your results.
264
And that probably means that the evidence
in your new data is not super strong.
265
And so it may indicate some issues with
your theory or some issues with your data.
266
And you have to collect more data to
figure out which of those it is basically.
267
And so it's, it's kind of helping you also
figure out the next steps in your
268
research, I feel, which is helpful.
269
But it can be frustrating, of course, and
harder to convince maybe co -authors and
270
reviewers to.
271
move forward with a paper like that.
272
But to me it is very interesting these
results from sensitivity analyses.
273
Yeah, yeah, completely agree in that.
274
That's very interesting to see the, yeah,
if the results differ on the priors, and
275
that can also help, you know, settle any
argument on the choice of prior.
276
You know, if people are really in
disagreement about which priors to choose,
277
well, then you can run the model with both
sets of priors, and if the results don't
278
change, it's like, well, let's stop
arguing.
279
That's kind of...
280
It's kind of silly.
281
We just lost time.
282
So let's just focus on the results then.
283
I think it's a very interesting framework.
284
And then there is another.
285
So that is like that entails running the
model, running MCMC on the model.
286
But there are some checks that you do
before that to ensure the robustness of
287
your patient models.
288
And one of that step is.
289
very crucial and called primary predictive
checks.
290
Can you talk about that to beat Sonja?
291
Yeah, so as you said, these checks happen
before you do any actual analysis.
292
So you can do them before you collect any
data.
293
In fact, one reason for using them is to
figure out whether the priors you came up
294
with results in sensible ranges of
possible parameter estimates, right?
295
In some cases, especially with these
complex multivariate models, your priors
296
may interact in unexpected ways and then
result in predictions that are not in line
297
with what your theory is actually telling
you you should expect.
298
And so prior predictive checks basically
until you specify your priors for all your
299
parameters.
300
And then you generate
301
parameter values from those priors by
combining it with your model
302
specification.
303
And then those combinations of parameter
estimates are used to generate what are
304
called prior predictive samples.
305
So these are samples of some pre
-specified size that represent possible
306
observations that align with what your
priors are conveying combined with your
307
model.
308
And so ideally,
309
those prior predictive samples look kind
of like what you would expect your data to
310
look like.
311
And sometimes for researchers, it is
easier to think about what the data should
312
look like compared to what the parameter
estimates can be.
313
And so in that sense, prior predictive
checks can be really helpful in checking
314
not just the priors, but checking the
researcher and making sure that they
315
actually convey their knowledge to me, for
example, correctly.
316
Yeah, did that answer your question?
317
Yeah, yeah, I think that's a great
definition and definitely encourage any
318
Bayesian practitioner to include prior
predictive checks in their workflow.
319
Once you have written a model, that should
be the first thing you do.
320
Do not run a CMC before doing prior
predictive checks.
321
And recently, I feel like a lot of the
software packages for Bayesian methods
322
have...
323
included very simple ways of running these
checks, which when I first started looking
324
at them, it was kind of more of a niche
step in the workflow.
325
And so it required a few more steps and
some more like coding, but now it's as
326
easy as just switching like a toggle to
get those prior predictive samples.
327
So that's great.
328
Yeah, yeah, yeah, completely agree.
329
That's also, yeah, it's definitely
something that's, that's been more and
330
more popular in the different
331
classes and courses that I teach, whether
it's online courses or live workshops,
332
always show prior predictive checks almost
all the time.
333
So yeah, it's becoming way, way more
popular and widespread.
334
So that's really good because I can tell
you when I work on a real model for
335
clients, always the first thing I do
before running MCMC is prior predictive
336
checks.
337
And actually there is a fantastic way
of...
338
you know, doing prior predictive checks,
like kind of industrialized and that's
339
called simulation based calibration.
340
Have you heard of that?
341
No, I mean, maybe the term, but I have no
idea what it is.
342
So that's just like making prior
predictive checks on an industrialized
343
scale.
344
Basically now instead of just
345
running through the model forward, as you
explained, and generate prior predictive
346
samples, what you're doing with SPC, so
simulation -based calibration, is
347
generating not only prior predictive
samples, but prior samples of the
348
parameters of the model.
349
You stock these parameters in some object.
350
but you don't give them to the model, but
you keep them somewhere safe.
351
And then the prior predictive samples, so
the plausible observations generated by
352
the model based on the prior samples that
you just kept in the fridge, these prior
353
predictive samples, now you're going to
consider them as data.
354
And you're going to tell the model, well,
run MCMC on these data.
355
as if we had observed these prior
predictive samples in the wild, because
356
that's what prior predictive samples are.
357
It's possible samples we could observe
before we know anything about real data.
358
So you feed that to the model.
359
You make the model run MCMC on that.
360
So that means backward inference.
361
So now the model is going to find out
about the plausible parameter values which
362
could have generated this data.
363
And then what you're going to do is
compare the posterior
364
distribution that the model inferred for
the parameter values to the true parameter
365
values that you kept in the fridge before.
366
You're going to get, so these parameter
values are true.
367
So you just have one of them, because it's
just one sample from the prior parameters.
368
And you're going to compare these value,
these value to the distribution of
369
posterior parameters that you just got
from the model.
370
And based on that,
371
and how far the model is from the true
parameter, you can find out if your model
372
is biased or if it's well calibrated.
373
And that's a really great way to be much
more certain that the model is able to
374
recover what you want it to recover.
375
basically playing God, and then you're
trying to see if the model is able to
376
recover the parameters that you use to
generate the data.
377
And not only will you do that once, but
you want to do that many times, many, many
378
times, because, well, the more you do it,
then you enter a kind of a frequentist
379
realm, right?
380
Where you're like, you just repeat the
experiments a lot.
381
And then that's how you're going to see
how calibrated the model is, because then
382
you can do some calibration plots.
383
there are a lot of metrics around that
it's a kind of a developing area of the
384
research but there are a lot of metrics
and one of them is basically just plotting
385
the true parameter values and well for
instance the mean posterior value from the
386
parameter and then if this mean is most of
the time along the the line x equals y
387
well that means you are in pretty good
shape you are but I mean it's the mean
388
here you
389
So you have to look at the whole
distribution, but that's to give you an
390
idea.
391
And so the bottleneck is you want to do
that a lot of time.
392
So you have to run MCMC a lot of times.
393
Most of the time, if you're just doing a
regression, that should be okay.
394
But sometimes it's going to take a lot of
time to run MCMC and it can be hard.
395
In these cases, you have new algorithms
that can be efficient because there is one
396
called
397
amortized Bayesian inference, a method
called amortized Bayesian inference.
398
We just covered that in episode 107 with
Marvin Schmidt.
399
And basically that's exactly a use case
for amortized Bayesian inference because
400
the model doesn't change, but the data
changes in each iteration of the loop.
401
And so what amortized Bayesian inference
is doing is just, well, just is training a
402
deep neural network on the model.
403
as a first step.
404
And then the second step is the inference,
but the inference is just instantaneous
405
because you've trained the deep neural
network.
406
And that means you can do, you can get as
black, almost as many poster samples as
407
you want.
408
Once you have trained the deep neural
network.
409
And so that's why it's almost all
inspection inference.
410
And that's a perfect use case for SBC
because then like you can just like you
411
get new, a new,
412
new samples for free.
413
And actually, so I definitely encourage
people to look at that.
414
It's still developing.
415
So right now you cannot, for instance, use
Baseflow, which is the Python package that
416
Marvin talked about in 1 .07 with PIMC,
but it's something we're working on.
417
And the goal is that it's completely
compatible.
418
But yeah, like I'll link to the tutorial
notebook in the show notes for people.
419
who want to get an idea of what SPC is
because even though you're not applying it
420
right now at least you have that in mind
and you know what that means and you can
421
work your way to out that.
422
Yeah that's amazing.
423
I feel like one of the biggest hurdles in
the structural equation modeling approach
424
with using Bayesian is just the time
commitment.
425
I'm
426
There is one analysis I was running and it
takes, I think for one analysis, it takes
427
almost a week to run it because it's a big
sample and then it's a complicated model.
428
And so if I would have to rerun that model
a thousand times, it would not be fun.
429
so knowing that there's maybe some options
on the horizon to help us speed along that
430
process would be, I think that would
change our field for sure.
431
So that's very exciting.
432
Yeah, yeah, yeah.
433
That's really super exciting.
434
And that's why I'm also super enthusiastic
about the desalmatized Bayesian infant
435
stuff, because I discovered that in
episode 107, so it's not a long time ago.
436
But as soon as I heard about that, I dug
into it, because that's super interesting.
437
Yeah.
438
I'm going to read about it after we finish
recording this.
439
Yeah, yeah, for sure.
440
And feel free to send me any questions.
441
And I find it's also a very elegant way to
marry the Bayesian framework in the deep
442
neural network methods.
443
So I really love that.
444
It's really elegant and promising, as you
were saying.
445
Talking about SCM, so structural equation
modeling, do you find that Bayesian
446
methods help?
447
in for these kind of models and especially
when it comes to educational research
448
which is one of your fields?
449
Yes, I think Bayesian methods can sort of
help on both ends of the spectrum that we
450
see with educational data which is either
we have very small samples and so
451
researchers still have these ambitious
theoretical models that they want to test.
452
but it's just not doable with frequentist
estimators.
453
And so based with the priors, it can help
a little bit to boost the information that
454
we have, which is really nice.
455
And then on the other side, ever since
starting this position and moving into a
456
college of education, I've been given
access to many large data sets that have
457
very complicated nesting structures.
458
That's something you see all the time in
education.
459
You have
460
schools and then teachers and students and
the students they change teachers because
461
it's also longitudinal so there's a time
component and all of these different
462
nested structures can be very hard to
model using estimators like nextman
463
likelihood and bayesian methods not
necessarily structural equation modeling
464
but maybe more a hierarchical linear model
or some other multi -level approach it can
465
be super flexible to handle all of those
466
structures and still give people results
that they can use to inform policy.
467
Because that's something in education that
I didn't really see when I was still in
468
the department of psychology before is
that a lot of the research here is really
469
directly informing what is actually going
to happen in schools.
470
And so it's really neat that these
Bayesian methods are allowing them to
471
answer much more complicated research
questions and really make use of all of
472
the data that they have.
473
So that's been really exciting.
474
And actually, I wanted to ask you
precisely what the challenges you face
475
with longitudinal data and how do you
address these challenges because I know
476
that can be pretty hard.
477
I think with longitudinal data, the
biggest challenge actually doesn't have
478
anything to do with the estimator.
479
It is more just inherent in longitudinal
data, which is that we will always...
480
unless you have a really special sample,
but we will always have missing data.
481
Participants will always drop out at some
point or just skip a measurement.
482
And of course, other estimation methods
also have options for accommodating
483
missing data, such as full information
maximum likelihood.
484
But I find that the Bayesian approach
where you can do imputation while you're
485
estimating, so you're just imputing the
data at every posterior sample, is very
486
elegant, efficient.
487
and easy for researchers to wrap their
minds around.
488
And it still allows you just like with
other multiple imputation methods to
489
include an sort of auxiliary model
explaining the missingness, which helps
490
with the like missing at random, type data
that we deal with a lot.
491
And so I feel that that is especially
exciting.
492
I honestly started thinking about this
more deeply when I started my position
493
here and I met my new colleague.
494
Dr.
495
Brian Keller, he is working on some
software, it's called BLIMP, which I think
496
it stands for Bayesian Latent Interaction
Modeling Program, I want to say.
497
So it's actually created for modeling
interactions between latent variables,
498
which is a whole other issue.
499
But within that software, they actually
also created a really powerful method for
500
dealing with missing data, or not
necessarily the method, but just the
501
application of it.
502
And so...
503
Now that I've met him and he's always
talking about it, it makes me think about
504
it more.
505
So that's very exciting.
506
Yeah, for sure.
507
And feel free to add a link to this
project to Blimp in the show notes,
508
because I think that's going to be very
interesting to listeners.
509
And how, I'm wondering if patient methods
improve...
510
the measurement and the evaluation
processes in educational settings, because
511
I know it's a challenge.
512
Is that something that you're working on
actively right now, or you've done any
513
projects on that that you want to talk
about?
514
Well, I teach measurement to grad
students.
515
So it's not necessarily that I get to talk
about Bayes a lot in there.
516
But what I'm realizing is that
517
When we talk about measurement from a
frequentist standpoint, we typically start
518
with asking students a bunch of questions.
519
Let's say we're trying to measure math
ability.
520
So we ask them a bunch of math questions.
521
Then if we use frequentist estimation, we
can use those item responses to generate
522
some sort of probability of those
responses giving some underlying level of
523
math ability.
524
So how probable is it that they gave these
answers given this level of math?
525
But actually what we want to know is what
is the student's math ability, given the
526
patterns of observed responses.
527
And so Bayes theorem gives us a really
elegant way of answering exactly that
528
question, right.
529
Instead of the opposite way.
530
And so I think in a big way, Bayesian
methods just align better with how people
531
already think about the research that
they're doing or the thing, the questions
532
that they're, they want to answer.
533
I think.
534
This is also a reason why a lot of
researchers struggle with getting the
535
interpretation of things like a confidence
interval correct, right?
536
It's just not intuitive.
537
Whereas Bayesian methods, they are
intuitive.
538
And so in that sense, I think not so much
like estimation wise, but just
539
interpretation wise, Bayesian methods can
help a lot in our field.
540
And then in addition to that, I think when
we do use Bayesian estimation,
541
those posterior distributions, they can
give us so much more information about the
542
parameters of interest that we are
interested in.
543
And they can also help us understand what
future data would look like given those
544
posteriors, right?
545
If we move from like prior predictors to
posterior predictors, which are these
546
samples generated from the posteriors,
that should look like our data should look
547
like that data, right?
548
If our model is doing a good job of
representing our data.
549
And so,
550
I think that's an exciting extension of
Bayes as well.
551
It gives us more tools to evaluate our
model and to make sure that it's actually
552
doing a good job of representing our data,
which is especially important in
553
structural equation modeling, where we
rely very heavily on global measures of
554
fit.
555
And so this is a really nice new tool for
people to use.
556
I see.
557
Okay.
558
Yeah.
559
I am.
560
I need to know about that in particular.
561
That's...
562
That's very interesting.
563
Yeah.
564
So I mean, I would have more questions on
that, but I want to ask you in particular
565
on a publication you have about under
-fitting and over -fitting.
566
And you've looked at the performance of
Bayesian model selection in SEM.
567
I find that super interesting.
568
So can you summarize the key findings of
this paper and...
569
their application, their implications for
researchers using SEM?
570
Yeah, for sure.
571
This is a really fun project for me to
work on, kind of an extension of my
572
dissertation.
573
So it made me feel like, I'm really moving
on, creating a program of research.
574
So yeah, thanks for asking about the
paper.
575
So yeah, as I already kind of mentioned,
within structural equation modeling,
576
Researchers rely really heavily on these
model selection and fit indices to make
577
choices about what model they're going to
keep in the end.
578
A lot of the times, researchers come in
with some idea of what the model would
579
look like, but they are always tinkering a
little bit.
580
They're ready to know that they're wrong
and they want to get to a better model.
581
And so the same is true when we use
Bayesian estimation and we have sort of a
582
similar set of indices to look at.
583
in terms of the fit of a single model or
comparing multiple models and selecting
584
the best one.
585
And so very typically those indices are
tested in terms of how well they can
586
identify underfit.
587
And so underfit occurs when you forgot to
include a certain parameter.
588
So your model is too simple for the
underlying data generating mechanism.
589
You forgot something.
590
And so all of these indices generally
work.
591
pretty well, and that's also what we found
in our study in terms of selecting the
592
correct model when there are some
alternatives that have fewer parameters or
593
picking up on the correct model fitting
well by itself versus models that forget
594
these parameters.
595
But what we were really interested in is
looking at, OK, how well do these indices
596
actually detect overfitting?
597
So that's where you add parameters that
you don't really need.
598
So you're making your model overly
complex.
599
And when we have models that are too
complex, they tend not to generalize to
600
new samples, right?
601
They're optimized for our specific sample
and that's not really useful in science.
602
So we want to make sure that we don't keep
going and like adding paths and making our
603
models super complicated.
604
And so surprisingly what we found across
like a range of over fitting scenarios is
605
that they do not really do a good job of
detecting any of this.
606
Most indices, if anything, just make the
model look better and better and better.
607
Even some of these indices, like model
selection indices, will have a penalty
608
term in their formula that's supposed to
penalize for having too many parameters,
609
right?
610
For making your model too complex.
611
And even those were just like, yeah, this
is fine.
612
Keep going, keep going.
613
And so that's a little bit worrisome.
614
And I think...
615
We really need to think about developing
some new ways of detecting when we go too
616
far, right?
617
Figuring out at what point we need to stop
in our model modification, which is
618
something that researchers really love to
do, especially in structural equation
619
modeling.
620
I won't speak for any other areas.
621
And so, yeah, I think there's a lot of
work to be done.
622
And I was very surprised that these
indices that are supposed to help us
623
detect overfitting also didn't really do.
624
a good job.
625
And so I'm excited to work more on this.
626
I would say in general, if people want an
actionable takeaway, it is always helpful
627
when you have multiple models to compare
versus just your one model of interest.
628
It will help you tease, sort of figure out
better, which one is the correct one
629
versus just is your model good enough?
630
And so that would be my, my advice for
researchers.
631
Yeah.
632
Yeah, definitely.
633
I always like having a very basic and dumb
looking linear regression to compare to
634
that and build my way on top of that
because you can already do really cool
635
stuff with plain simple linear regression
and why making it harder if you cannot
636
prove, you cannot discern a particular
effect of...
637
of the new method you're applying.
638
Yeah.
639
And so do you have then from from your
dive into these, do you have some fit
640
indices that you recommend?
641
And how do they compare to traditional fit
indices?
642
So I think for model
643
fit of a single model within structural
equation modeling.
644
The most popular ones are called
comparative fit index, the Tucker Lewis
645
index, and then the root mean square error
of approximation.
646
You'll see these in like every single
paper published.
647
And so there are Bayesian versions of
those indices, but based on all my
648
research using those so far,
649
I would actually not recommend those at
all for evaluating the fit of your
650
specific model.
651
It seems from at least my research that
they are very sensitive to your sample
652
size, which means that as you get a larger
and larger sample, your model will just
653
keep looking better and better and better
and better, even if it's wrong.
654
So something that would be flagged as like
a...
655
a misspecified model with a small sample
might look perfectly fine with a large
656
sample.
657
And so that's not what you want, right?
658
You want the fit index to reflect the
misspecification, not your sample size.
659
And so I was really excited when these
were first introduced, but I think we need
660
a lot more knowledge about how to actually
use them before they are really useful.
661
And so my advice for researchers who want
to know something about their fit is
662
really to look at
663
the posterior predictive checks.
664
And within structural equation modeling,
I'm not sure how widespread this is for
665
other methods, but we have something
called a posterior predictive p -value,
666
where we basically take our observed data
and evaluate the fit of that data to our
667
model at each posterior iteration.
668
For example, using a likelihood ratio test
or like a chi -square or something.
669
And then we do the same for a posterior
predicted sample.
670
using this in within each of those samples
as well.
671
And the idea is that if your model fits
your data well, then about half of the
672
predictive samples should fit better and
the other half should fit worse, right?
673
Yours should be nicely cozy in the middle.
674
If all of your posterior predictive
samples fit worse than your actual data,
675
then it's an indication that you are
overfitting, right?
676
Like,
677
the model will never fit as well as it
does for your specific data.
678
And so I think in that sense, that index
could potentially give some idea of
679
overfitting, although again, in our study,
we didn't really see that happening.
680
But I think it's a more informative method
of looking at fit within Bayesian
681
structural equation modeling.
682
And so even though it's kind of old
school, I think it's still probably the...
683
the best option for researchers to look
at.
684
Okay, yeah, thanks.
685
That's like, I love that.
686
That's very practical.
687
And I think listeners really appreciate
that.
688
I have like, I was wondering about SEMs
again, and if you have an example from
689
your research where Bayesian SEM provided
significant insights that
690
traditional methods might have missed.
691
Yeah, so some work I'm working on right
now is with a group of researchers who are
692
really interested in figuring out how
strong the evidence is that there is no
693
effect, right?
694
That some path is zero within a bigger
structural model.
695
And with frequentist analysis, all we can
really do is fail to reject the known,
696
right?
697
We have an absence of evidence.
698
but that doesn't mean that there's
evidence of absence.
699
And so we can't really quantify like how
strong or how convinced we should be that
700
that null is really a null effect.
701
But with Bayesian methods, we have base
factors, right?
702
And we can actually explicitly test the
evidence in favor of the estimate being
703
zero versus the estimate being not zero,
right?
704
Either smaller or larger than zero.
705
And so that's really...
706
When I talked to the applied researchers,
once they came to me with this problem,
707
which started as just like a structural
equation modeling problem, but then I was
708
like, well, have you ever considered using
Bayesian methods?
709
Because I feel like it could really help
you get at that question.
710
Like how strong is that evidence relative
to the evidence for an effect, right?
711
And so we've been working on that right
now and it is very interesting to see the
712
results and then also to communicate that
with them and see.
713
They get so excited about it.
714
So that's been fun.
715
Yeah, for sure.
716
That's super cool.
717
And you don't have anything to share in
the show notes yet, right?
718
Not yet.
719
No, I'll keep you posted.
720
Yeah, for sure.
721
Because maybe by the time of publication,
you'll have something for us.
722
Yes.
723
And now I'd like to talk a bit about
your...
724
your teaching because you teach a lot of
classes.
725
You've talked a bit about that already at
the beginning of the show, but how do you
726
approach teaching Bayesian methods to
students in your program, which is the
727
statistics measurement and evaluation and
indication program?
728
Yeah, so I got to be honest and say I have
never taught an entire class on Bayesian
729
methods yet.
730
I'm very excited that I just talked with
my colleagues and I got the okay to
731
develop it and put it on the schedule.
732
So it's coming.
733
But I did recently join a panel
discussion, which was about teaching
734
Bayesian methods.
735
It was organized by the Bayesian Education
Research and Practice Section of the ISBA
736
Association.
737
And so the other two panelists, I was
really starstruck.
738
to be honest, were E .J.
739
Wagemakers and Joachim van de Kerkoven,
which are like, to me, those are really
740
big names.
741
And so talking to them, I really learned a
lot during that panel.
742
I felt like I was more on the panel as a
as an audience member, but it was great
743
for me.
744
And and so from that, I think if I do get
to teach a class on Bayesian methods,
745
which hopefully will be soon.
746
I think I really want to focus on showing
students the entire Bayesian workflow,
747
right?
748
Just as we were talking about, starting
with figuring out priors, prior predictive
749
checks, maybe some of that fancy
calibration.
750
And then also doing sensitivity analyses,
looking at the fit with the posterior
751
predictive samples, all of that stuff.
752
I think...
753
For me, I wouldn't necessarily combine
that with structural equation models
754
because those are already pretty
complicated models.
755
And so I think within a class that's
really focused on Bayesian methods, I
756
would probably stick to a simple but
general model, such as a linear regression
757
model, for example, to illustrate all of
those steps.
758
Yeah, I've been just buying, like I have a
whole bookshelf now of books on Bayesian
759
and teaching Bayesian.
760
And so I'm excited to start reading those.
761
developing my class soon yeah that's super
exciting well done congrats on that i'm
762
glad to hear that so first eg vagon makers
was on the show i don't remember which
763
episode but i will definitely link to it
in the show notes and second yeah which
764
books are you are you gonna use well
765
Good question.
766
So there's one that I kind of like, but it
is very broad, which is written by David
767
Kaplan, who's at the University of
Wisconsin Madison.
768
And it's called, I think, vision
statistics for the social sciences.
769
And so what I like about it is that many
of the examples that are used throughout
770
the book are very relevant to the students
that I would be teaching.
771
And it also covers a wide range.
772
of models, which would be nice.
773
But now that I've like philosophically
switched more to this workflow
774
perspective, it's actually a little bit
difficult to find a textbook that covers
775
all of those.
776
And so I may have to rely a lot on some of
the online resources.
777
I know there's some really great posts by,
I'm so bad with names.
778
I want to say his name is Michael
something.
779
Where he talks about workflow.
780
Yes, probably.
781
Yes, that sounds familiar.
782
His posts are really informative and so I
would probably rely on those a lot as
783
well.
784
Especially because they also use
relatively simpler models.
785
I think, yeah, for some of the components
of the workflow that they just haven't
786
been covered in textbooks as much yet.
787
So if anyone is writing a book right now,
please add some chapters on those lesser
788
known.
789
components, that would be great.
790
Yeah.
791
Yeah, so there is definitely Michael
Bedoncourt's blog.
792
And I know Andrew Gelman is writing a book
right now about the Bayesian workflow.
793
So the Bayesian workflow paper.
794
Yeah, that's a good paper.
795
Yeah, I'll put it in the show notes.
796
But basically, he's turning that into a
book right now.
797
Amazing.
798
Yeah, so it's gonna be perfect for you.
799
And have you taken a look at his latest
book, Active Statistics?
800
Because that's exactly for preparing
teachers to teach patient stats.
801
Yes, he has like an I feel like an older
book as well where he has these
802
activities, but it's really nice that he
came out with this newer, more recent one.
803
I haven't read it yet, but it's on my
804
on my to buy list.
805
I have to buy these books through the
department, so it takes a while.
806
Yeah, well, and you can already listen to
episode 106 if you want.
807
He was on the show and talked exactly
about these books.
808
Amazing.
809
I'll put it in the show notes.
810
And what did we talk about?
811
There was also Michael Betancourt, E .G.
812
Wagenmarkers,
813
Active statistics, microbed and code,
yeah, and the Bayesian workflow paper.
814
Yeah, thanks for reminding me about that
paper.
815
Yeah, it's a really good one.
816
I think it's going to be helpful.
817
I'm not sure they cover SBC already, but
that's possible.
818
But SBC, in any case, you'll have it in
the Bayes flow tutorial that I already
819
linked to in the show notes.
820
So I'll put out that.
821
And actually, what are future developments
in Bayesian stats that excite you the
822
most, especially in the context of
educational research?
823
Well, what you just talked about, and this
amortized estimation thing is very
824
exciting to me.
825
I think, as I mentioned, one of the
biggest hurdles for people switching to
826
Bayesian methods is just the time
commitment, especially with structural
827
equation models.
828
And so knowing that people are working on
algorithms that will speed that up, even
829
for a single analysis, it's just really
exciting to me.
830
And in addition to that, sort of in a
similar vein, I think a lot of smart
831
people are working on software, which is
lowering barriers to entry.
832
People in education, they know a lot about
education, right?
833
That's their field, but they don't have
time to really dive into.
834
Bayesian statistics.
835
And so for a long time, it was very
inaccessible.
836
But now, for example, as you already
mentioned, Ed Merkel, he has his package
837
Blavan, which is great for people who are
interested in structural equation modeling
838
and Bayesian methods.
839
And sort of similarly, you have that
Berkner has that BRMS package.
840
And then if you want to go even more
accessible, there's JASP.
841
which is that point and click sort of
alternative to SPSS, which I really enjoy
842
showing people to let them know that they
don't need to be afraid that they'll lose
843
access to SPSS at some point in their
life.
844
So I think those are all great things.
845
And in a similar vein, there are so many
more online resources now.
846
Then when I first started learning about
base, like when people have questions or
847
they want to get started, I have so many
links to send them of like papers, online
848
courses, YouTube videos, podcasts like
this one.
849
and so I think that's, what's really
exciting to me, not so much what we're
850
doing behind the scenes, right?
851
The actual method itself, although that's
also very exciting, but for working with
852
people.
853
in education or other applied fields.
854
I'm glad that we are all working on making
it easier.
855
So, yeah.
856
Yeah.
857
So first, thanks a lot for recommending
the show to people.
858
I appreciate it.
859
And yeah, completely resonate with what
you just told.
860
Happy to hear that the educational efforts
are.
861
useful for sure that's something that's
very dear to my heart and I spend a lot of
862
time doing that so my people and yeah as
you are saying it's already hard enough to
863
know a lot about educational research but
if you have to learn a whole new
864
statistical framework from scratch it's
very hard and more than that it's not
865
really valued and incentivized in the
academic realm so like why would you even
866
spend time doing that?
867
you'd much rather write a paper.
868
So that's like, that's for sure that's an
issue.
869
So yeah, definitely working together on
that is definitely helping.
870
And on that note, I put all the links in
the show notes and also Paul Burkner was
871
on the show episode 35.
872
So for people who want to dig deeper about
Paul's work, especially BRMS, as you
873
mentioned Sonia.
874
definitely take a well give a give a
listen to that to that episode and also
875
for people who are using Python more than
are but really like the formula syntax
876
that BRMS has you can do that in Python
you can use a package called BAMI and it's
877
basically BRMS in in Python in the
878
that's built on top of PimC and that's
built by a lot of very smart and cool
879
people like my friend Tomica Pretto.
880
He's one of the main core developers.
881
I just released actually an online course
with him about advanced regression in
882
Bambi and Python.
883
So it was a fun course.
884
We've been developing that for the last
two years and we released that this week.
885
So I have to say I'm quite relieved.
886
Congratulations.
887
Yeah, that's exciting.
888
Yeah, that was a very fun one.
889
It's just, I mean, it took so much time
that because we wanted something that was
890
really comprehensive and as evergreen as
it gets.
891
So we didn't want to do something, you
know, quick and then having to do it all
892
over again one year later.
893
So I wanted to take our time and basically
take people from normal linear regression
894
and then okay, how do you generalize that?
895
How do you handle?
896
non -normal likelihoods, how do you handle
several categories?
897
Because most of the examples out there in
the internet are somewhat introductory.
898
How do you do Poisson regression and
binomial regression most of the time?
899
But what about the most complex cases?
900
What happens if you have zero inflated
data?
901
What happens if you have data that's very
dispersed that a binomial or a Poisson
902
cannot handle?
903
What happens if you have multi -category
called data?
904
More than two categories.
905
You cannot use the binomial.
906
You have to use the category called all
the multinomial distributions.
907
And these ones are harder to handle.
908
You need another link function that the
inverse logit.
909
So it's a lot of stuff.
910
But the cool thing is that then you can do
really powerful models.
911
And if you marry that with hierarchical
models, that is really powerful stuff that
912
you can do.
913
So yeah, that's what the whole course is
about.
914
I'll have Tommy actually on the show to
talk about that with him.
915
So that's going to be a fun one.
916
Yeah, I'm looking forward to hearing more
about it.
917
Sounds like something I might recommend to
some people that I know.
918
Yeah, yeah.
919
that's exciting.
920
Yeah, yeah, for sure.
921
Happy to.
922
Happy to.
923
like send you send you the link I put the
link in the show notes anyway so that
924
people who are interested can can take a
look and of course patrons of the show
925
have a 10 % discount because they are they
are the best listeners in the world so you
926
know they deserve a gift yes they are well
Sonya I've already taken quite a lot of
927
your time so we're gonna we're gonna start
closing up but
928
I'm wondering if you have any advice to
give to aspiring researchers who are
929
interested in incorporating Bayesian
methods into their own work and who are
930
working in your field, so educational
research?
931
Yeah, I think the first thing I would say
is don't be scared, which I say a lot when
932
I talk about statistics.
933
Don't be scared and take your time.
934
I think...
935
A lot of people may come into Bayesian
methods after hearing about frequentist
936
methods for years and years and years.
937
And so it's going to take more than a week
or two to learn everything you need to
938
know about Bayes, right?
939
That's normal.
940
We don't expect to familiarize ourselves
with a whole new field in a day or a week.
941
And that's fine.
942
Don't feel like a failure.
943
Then.
944
I don't know, I would also try and look
for papers in your field, right?
945
Like if you're studying school climate, go
online and search for school climate base
946
and see if anyone else has done any work
on your topic of interest using this new
947
estimation method.
948
It's always great to see examples of how
other people are using it within a context
949
that you are familiar with, right?
950
You don't have to start reading all these
technical papers.
951
You can stay within your realm of
knowledge, within your realm of expertise,
952
and then just eke out a little bit.
953
And then after that, I mean, as we just
talked about, there are so many resources
954
available that you can look for, and a lot
of them are starting to become super
955
specific as well.
956
So if you are interested in structural
equation models, go look for resources
957
about Bayesian structural equation
modeling.
958
But if you're interested in some other
model, try and find resources specific to
959
those.
960
And as you're going through this process,
a nice little side benefit that's going to
961
happen is that you're going to get really
good at Googling because you've got to
962
find all this information.
963
But it's out there and it's there to find.
964
So, yeah, that would really be my advice.
965
Don't be scared.
966
Yeah, it's a good one.
967
That's definitely a good one because
then...
968
Like if you're not scared to be
embarrassed or fail, you're gonna ask a
969
lot of questions, you're gonna meet
interesting people, you're gonna learn way
970
faster than you thought.
971
So yeah, definitely great advice.
972
Thanks, Sonja.
973
And people in our field, Invasion Methods,
they are so nice.
974
I feel like they are just so excited
when...
975
I'm so excited when anyone shows any
interest in what I do.
976
Yeah, don't be scared to reach out to
people either because they're going to be
977
really happy that you did.
978
True, true.
979
Yeah, very good point.
980
Yeah, I find that community is extremely
welcoming, extremely ready to help.
981
And honestly, I still have to find trolls
in that community.
982
That's really super value.
983
I feel like it helps that a lot of us came
into this area through also kind of like a
984
roundabout way, right?
985
I don't think anyone is born thinking
they're going to be a Beijing statistician
986
and so we understand.
987
Yeah, yeah.
988
Yeah, well, I did.
989
I think my first word was prior.
990
So, you know, okay.
991
Well, you're the exception to the rule.
992
Yeah, yeah.
993
But you know, that's life.
994
I'm used to being the black sheep.
995
That's fine.
996
no, I think I wanted to be a football
player or something like that.
997
no, also I wanted to fly planes.
998
I wanted to be a fighter pilot at some
point later after I had outgrown football.
999
You're a thrill seeker.
Speaker:
I wanted to be a vet or something, but
then I had to take my pets to the vet and
Speaker:
they were
Speaker:
bleeding and I was like, no, I don't want
the event anymore.
Speaker:
Well, it depends on the kind of animals
you treat, but veterinarian can be a
Speaker:
thrill seeking experience too.
Speaker:
You know, like if you're specialized in
snakes or grizzlies or lions, I'm guessing
Speaker:
it's not all the time, you know, super,
super easy and tranquil.
Speaker:
no.
Speaker:
Awesome.
Speaker:
Well Sonia, that was really great to have
you on the show.
Speaker:
Of course, I'm going to ask you the last
two questions.
Speaker:
Ask every guest at the end of the show.
Speaker:
So if you had unlimited time and
resources, which problem would you try to
Speaker:
solve?
Speaker:
I thought about this a lot because I
wanted to solve many problems.
Speaker:
So when I give this answer, I'm hoping
that other people are taking care of all
Speaker:
those other problems.
Speaker:
But I think something that I've noticed
recently is that a lot of people seem to
Speaker:
have lost the ability or the interest in
critical thinking and being curious and
Speaker:
trying to figure out things by yourself.
Speaker:
And so that's something that I would like
to.
Speaker:
solve or improve somehow?
Speaker:
Don't ask me how, but I think being a
critical thinker and being curious are two
Speaker:
really important skills to have to succeed
in our society right now.
Speaker:
I mean, there's so much information being
thrown at us that it's really up to you to
Speaker:
figure out what to focus on and what to
ignore.
Speaker:
And for that, you really need this
critical thinking skill and...
Speaker:
and also the curiosity to actually look
for information.
Speaker:
And so I think that's, it's also a very
educational problem, I feel.
Speaker:
So if it's where I am right now in my
career, but yeah, that would be something
Speaker:
to solve.
Speaker:
Yeah.
Speaker:
Completely understand that was actually my
answer also.
Speaker:
So I like, really?
Speaker:
Yeah.
Speaker:
Yeah.
Speaker:
Yeah.
Speaker:
I completely agree with you.
Speaker:
Yeah.
Speaker:
These are topics I found.
Speaker:
I find them.
Speaker:
I find super interesting.
Speaker:
How do you.
Speaker:
do we teach critical thinking, how do we
teach the scientific methods, things like
Speaker:
that.
Speaker:
It's always something I'm super excited to
talk about.
Speaker:
Yeah, I also hope it will have some sort
of trickle down effect on all the other
Speaker:
problems, right?
Speaker:
Once the whole world is very skilled at
critical thinking, all the other issues
Speaker:
will be resolved pretty quickly.
Speaker:
Yeah, not only because it's directly
solved, but...
Speaker:
I would say mainly because then you have
maybe less barriers.
Speaker:
And so yeah, probably coming from that.
Speaker:
And then second question, if you could
have dinner with any great scientific
Speaker:
mind, dead, alive or fictional food.
Speaker:
So I ended up
Speaker:
Choosing Ada Lovelace who's like one of
the first or maybe the first woman who
Speaker:
ever worked in computer programming area.
Speaker:
I think she's very interesting I also
recently found out that she passed away
Speaker:
when she was only like 36 Which is like
I'm I'm getting at that age and she
Speaker:
already accomplished all these things By
the time she passed away and so now I'm
Speaker:
like, okay I gotta I gotta step it up, but
I would really love to talk to her about
Speaker:
just her experience.
Speaker:
being so unique in that very manly world
and in that very manly time in general, I
Speaker:
think it would be very interesting to hear
the challenges and also maybe some
Speaker:
advantages or like benefits that she saw,
like why did she go through all this
Speaker:
trouble to begin with?
Speaker:
Yeah, I think it would be an interesting
conversation to have for sure.
Speaker:
Yeah, yeah, definitely.
Speaker:
Yeah, great choice.
Speaker:
I think, I think somebody already
Speaker:
had answered.
Speaker:
I don't remember who, but yeah, it's not a
very common choice.
Speaker:
We can have a dinner party together.
Speaker:
Yeah, exactly.
Speaker:
That's perfect.
Speaker:
Fantastic.
Speaker:
Great.
Speaker:
Thank you.
Speaker:
Thank you so much, Sonja.
Speaker:
That was a blast.
Speaker:
I learned so much.
Speaker:
Me too.
Speaker:
You're welcome.
Speaker:
And well, as usual, I put resources and a
link to a website.
Speaker:
in the show notes for those who want to
dig deeper.
Speaker:
Thank you again, Sonia, for taking the
time and being on this show.
Speaker:
Yeah, thank you.
Speaker:
It was so much fun.
Speaker:
This has been another episode of Learning
Bayesian Statistics.
Speaker:
Be sure to rate, review, and follow the
show on your favorite podcatcher, and
Speaker:
visit learnbaystats .com for more
resources about today's topics, as well as
Speaker:
access to more episodes to help you reach
true Bayesian state of mind.
Speaker:
That's learnbaystats .com.
Speaker:
Our theme music is Good Bayesian by Baba
Brinkman, fit MC Lass and Meghiraam.
Speaker:
Check out his awesome work at bababrinkman
.com.
Speaker:
I'm your host.
Speaker:
Alex Andorra.
Speaker:
You can follow me on Twitter at Alex
underscore Andorra, like the country.
Speaker:
You can support the show and unlock
exclusive benefits by visiting Patreon
Speaker:
.com slash LearnBasedDance.
Speaker:
Thank you so much for listening and for
your support.
Speaker:
You're truly a good Bayesian.
Speaker:
Change your predictions after taking
information in.
Speaker:
And if you're thinking I'll be less than
amazing, let's adjust those expectations.
Speaker:
Let me show you how to be a good Bayesian
Change calculations after taking fresh
Speaker:
data in Those predictions that your brain
is making Let's get them on a solid
Speaker:
foundation