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#109 Prior Sensitivity Analysis, Overfitting & Model Selection, with Sonja Winter
Episode 109 • 25th June 2024 • Learning Bayesian Statistics • Alexandre Andorra
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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!

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Transcript

This is an automatic transcript and may therefore contain errors. Please get in touch if you're willing to correct them.

Transcripts

Speaker:

Priors represent a crucial part of the

Bayesian workflow, and actually a big

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:

reason for its power and usefulness.

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:

But why is that?

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:

How do you choose reasonable priors in

your models?

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What even is a reasonable prior?

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These are deep questions that today's

guest, Sonja Winter, will guide us

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:

through.

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an assistant professor in the College of

Education and Human Development of the

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:

University of Missouri, Sonia's research

focuses on the development and application

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:

of patient approaches to the analysis of

educational and developmental

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:

psychological data, with a specific

emphasis on the role of priors.

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What a coincidence!

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In this episode, she shares insights on

the selection of priors, prior sensitivity

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analysis, and the challenges of working

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with longitudinal data.

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She also explores the implications of

Bayesian methods for model selection and

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fit indices in structural equation

modeling, as well as the challenges of

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detecting overfitting in models.

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When she's not working, you'll find Sonja

baking delicious treats, gardening, or

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watching beautiful birds.

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:

This is Learning Bayesian Statistics,

episode.

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:

Welcome to Learning Bayesian Statistics, a

podcast about Bayesian inference, the

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:

methods, the projects, and the people who

make it possible.

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I'm your host, Alex Andorra.

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You can follow me on Twitter at alex

.andorra, like the country.

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:

For any info about the show, learnbasedats

.com is Laplace to be.

27

:

Show notes, becoming a corporate sponsor,

unlocking Bayesian Merge, supporting the

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:

show on Patreon, everything is in there.

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:

That's learnbasedats .com.

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:

If you're interested in one -on -one

mentorship, online courses, or statistical

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:

consulting, feel free to reach out and

book a call.

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at topmate .io slash alex underscore and

dora see you around folks and best patient

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wishes to you all.

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:

Hello my dear patients, today I want to

thank the fantastic Jonathan Morgan and

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:

Francesco Madrisotti for supporting the

show on Patreon.

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:

Your support is invaluable and literally

makes this show possible.

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:

can't wait to talk with you guys in the

Slack channel.

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:

Second, with my friends and fellow PymC

core developers, Ravin Kumar and Tommy

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:

Capretto, we've just released our new

online course, Advanced Regression with

40

:

Bambi and PymC.

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:

And honestly, after two years of

development, it feels really great to get

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:

these out into the world, not only because

it was, well, long and intense, but mainly

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because I am so proud of the level of

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:

of details, teachings, and exercises that

we've packed into this one.

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It's basically the course I wish I had

once I had gone through the beginner's

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:

phase when learning patience tests, that

moment when you're like...

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Okay, I know how to do basic models, but

where do I go from here?

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I remember feeling quite lost, so we

wanted to give you a one -stop shop for

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such intermediate models with the most

content possible, as evergreen as it gets.

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If that sounds interesting, go to

intuitivebase .com and check out the full

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syllabus.

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We're enrolling the first cohort as we

speak!

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:

Of course, you get a 10 % discount if

you're a patron of the show.

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Go to the Patreon page or the Slack

channel to get the code.

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:

Okay, back to the show now and looking

forward to seeing you in the intuitive

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base discourse.

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Sonia Winter, welcome to Learning Bayesian

Statistics.

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Thank you.

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Thanks for having me.

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I'm really excited to talk to you today.

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Same, same.

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That's a treat.

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I have a lot of questions.

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I really love.

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like everything you're doing in your

research.

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We're going to talk a lot about priors

today, folks.

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So yeah, like get ready.

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But first, can you provide a brief

overview of your research interests and

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how patient methods play a role in your

work?

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Yeah, sure.

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So my background is actually in

developmental psychology.

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I did a bachelor or master's degree at

Utrecht University.

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And during that time, I really realized

that a lot of work needed to be done on

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the analysis part of social science

research.

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And so I switched and got really into

structural equation models, which are

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these big multivariate models that include

latent variables.

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I'm sure we'll talk more about that later.

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But those models can be hard to estimate

and there are all these issues.

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And so I was introduced to Bayesian

statistics.

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right after my master's degree when I was

working with Rens van der Schoot, also at

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Utrecht University.

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And he asked me to do this big literature

review about it with him.

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And that really introduced me.

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And so now I focus a lot on Bayesian

estimation and how it can help us estimate

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these structural equation models.

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And then specifically more recently, I've

really been focusing on how those priors

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can really help us.

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both with estimation and also just with

understanding our models a little bit

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better.

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So yeah, I'm really excited about all of

that.

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Yeah, I can guess that sounds awesome.

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So structural equation modeling, we

already talked about it on the show.

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So today we're going to focus a bit more

on priors and how that fits into the SEM

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framework.

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So for people who don't know about SEM, I

definitely recommend episode 102 with Ed

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Merkel.

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And we talked exactly about structural

equation modeling and causal inference in

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psychometrics.

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So that will be a.

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a very good introduction i think to these

topics for people and what i'm curious

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about sonia is you work a lot on priors

and things like that but how how did you

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end up working on that was something that

you were always curious about or that

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something that appeared later later on in

your in your phd studies

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I would say definitely something that

started or piqued my interest a little bit

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later.

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I think so after I first got familiarized

with Bayesian methods, I was excited

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mostly by how it could help, like priors

could help us estimate, like avoid

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negative variances and those types of

things.

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But I saw them more as a pragmatic tool to

help with that.

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And I didn't really focus so much on that.

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I feel like I also was a little bit afraid

at the time of, you know, those

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researchers who talk a lot about, well, we

shouldn't really make our priors

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informative because that's subjective and

that's bad.

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And so I really typically use like

uninformative priors or like software

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defaults for a lot of my work in the

beginning.

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But then during my PhD studies, I

actually.

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Well, first of all, I worked with another

researcher, Sanaa Smith, who was also a

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PhD student at the time.

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And she was really intrigued by something

she found that these software defaults can

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really cause issues when you're,

especially when your data is like very

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small, it can, it can make your results

look wild.

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And so we worked on this paper together

and created a shiny app to demonstrate all

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of that.

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And that made me realize that maybe

uninformative priors.

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are not always the best way to go.

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And also a prior that looks informative in

one scenario might be relatively

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uninformative in another.

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And so I really started shifting my, my

perspective on priors and focusing more on

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how ignoring them is kind of like ignoring

the best part of Bayesian in my opinion,

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at this point.

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and so now I really want to look at how,

how they can help us and how we can be

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thoughtful.

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We don't want to drive our science by

priors, right?

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We want to learn something new from our

data, but we find that balance is really

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what I'm looking for now.

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Yeah, well, what a fantastic application

of updating your belief, right?

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From a meta standpoint, you just like

updated your priors pretty aggressively

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and also very rationally.

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That's really impressive.

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Well done.

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Because that's hard to do also.

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It's not something we like to do.

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So that's great.

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Well done on doing that.

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And actually now that you're on the other

side, how do you approach the selection of

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priors in your research and what advice do

you have for people new to Bayesian

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methods?

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Yeah, great question.

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I think at least within structural

equation modeling, we as like applied

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researchers are helped somewhat because

distributions, at least for priors, are

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sort of clear.

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Like you don't have to think too much

about them.

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And so you can immediately jump into

thinking about, okay, what level of

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information do I want to convey in those

priors?

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And I think whenever I'm working with

applied researchers, I try to strike a

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balance with them because I know they are

not typically comfortable using like super

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informative priors that are really narrow.

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And so I just asked them to think about,

well, what would be a reasonable range?

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Like if we are estimating a linear

regression parameter, what would that

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effect size look like?

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Right.

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It might be zero or it might be two, but

it's probably not going to be 20.

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And so we can.

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sort of shape our prior to align with

those sort of expectations about how

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probable certain values are versus others.

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It's a really, I don't know, interactive

process between me and the researcher to

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get this right, especially for those types

of parameters that they are really

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interested in.

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I think another type of parameter that is

more challenging for applied researchers

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are those that are placed on residual

variances, for example.

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Like people typically don't...

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think about the part of the outcome that

they can't explain that much.

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And so that's where I do rely a bit more

on sort of, I don't know, industry

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standard choices that are typically not

super informative.

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But then once we pick our like target

priors, I always advise the researcher to

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follow it up with a sensitivity analysis

to see.

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like how robust their findings are to

changes in those priorities, either making

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them more informative or less informative.

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And so yeah, that's really the approach I

take.

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Of course, if someone wants to go full

base and full informative and they have

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this, this wealth of previous research to

draw from, then I'm all for going, going

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that route as well.

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It's just not as common.

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Hmm.

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Hmm.

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Yeah, I see.

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in what, what are the...

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main difficulties you see from people that

you advise like that?

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Where do you see them having more defenses

up or just more difficulties because they

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have a hard time wrapping their head

around a specific concept?

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I think just all over, I think if anyone

has ever tried to do like a power analysis

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working with researchers, it's sort of a

similar concept because

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It is not, at least in my field or the

people I work with are not very typically

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already thinking about the exact parameter

estimates that they are expecting to see,

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right?

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They are just, they just go with the

hypothesis.

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I think these two things are correlated

and they might not even go as far as to

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think, is it positive or negative?

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So then once you ask them those questions,

it really forces them to go much deeper on

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their theory and really consider like.

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What is, what am I expecting?

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What is reasonable based on what I know

from, from previous studies or just

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experience.

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And that can be kind of challenging.

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It's, it's kind of, I think sometimes the

researchers might feel like I'm

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criticizing them for not knowing, but I

think that's perfectly normal to not know.

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Like we already have so many other things

to think about.

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But it definitely.

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is kind of a hurdle.

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Also the time commitment, I think, to

really consider the priors, especially if

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you're coming from a frequentist realm

where you just say, okay, maximum

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likelihood go.

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Not only do you not have to think about

the estimation, but then also your results

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are almost instant.

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And so that's always kind of a challenge

as well.

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I see.

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Yeah.

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Yeah.

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Definitely something also I seen, I seen

beginners.

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yeah, it, it really depends on also where

they are coming from, as you were saying.

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Yeah.

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I did.

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Your advice will depend a lot on that.

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yeah.

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Yeah.

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And actually you work also a lot on prior

sensitivity analysis.

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can you, can you tell people what that is?

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And the importance of it in your, in your

modeling workflow and.

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how you incorporate it into your research.

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Yeah.

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So a sensitivity analysis for priors is

something that you typically do after you

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run your main analysis.

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So you come up with your target set of

priors for all your parameters, estimate

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the model, look at the results, look at

the posteriors.

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And then in the next step, you think

about, well, how can I change these

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priors?

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in sort of meaningful ways, either making

them more informative, perhaps making them

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represent some other theory, making them

less informative as well.

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So making the influence of the prior

weaker in your results.

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And then you rerun your analysis for all

of those different prior scenarios, and

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then compare those results to the ones

that you actually obtained with your

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target analysis and your target priors.

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And the idea here is to see,

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how much your results actually depend on

those prior beliefs that you came into the

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analysis with.

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If you don't find any differences, then

you can say, well, my results are mostly

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influenced by my data, by the new evidence

that I obtained.

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They are robust to changes in prior

beliefs, right?

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It doesn't really matter what beliefs you

came into the analysis with.

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The results are going to be the same,

which is great.

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In other cases, you might find that your

results do change meaningfully.

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So for example, in effect that was

significant with your priors is no longer

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significant using a frequentist term here,

but hopefully people will understand once

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you change your priors.

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And that's, of course, is a little bit

more difficult to handle because what do

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you do?

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I want to say that the goal is not to

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use the sensitivity analysis to then go

back and change your priors and run the

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analysis again and report that in your

paper.

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That would be sort of akin to p -hacking.

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Instead, I think it just contextualizes

your findings.

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It's showing that the knowledge you came

into the analysis with is partially

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driving your results.

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And that probably means that the evidence

in your new data is not super strong.

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And so it may indicate some issues with

your theory or some issues with your data.

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And you have to collect more data to

figure out which of those it is basically.

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And so it's, it's kind of helping you also

figure out the next steps in your

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research, I feel, which is helpful.

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But it can be frustrating, of course, and

harder to convince maybe co -authors and

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reviewers to.

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move forward with a paper like that.

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But to me it is very interesting these

results from sensitivity analyses.

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Yeah, yeah, completely agree in that.

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That's very interesting to see the, yeah,

if the results differ on the priors, and

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that can also help, you know, settle any

argument on the choice of prior.

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You know, if people are really in

disagreement about which priors to choose,

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well, then you can run the model with both

sets of priors, and if the results don't

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change, it's like, well, let's stop

arguing.

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That's kind of...

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It's kind of silly.

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We just lost time.

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So let's just focus on the results then.

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I think it's a very interesting framework.

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And then there is another.

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So that is like that entails running the

model, running MCMC on the model.

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But there are some checks that you do

before that to ensure the robustness of

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your patient models.

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And one of that step is.

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very crucial and called primary predictive

checks.

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Can you talk about that to beat Sonja?

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Yeah, so as you said, these checks happen

before you do any actual analysis.

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So you can do them before you collect any

data.

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In fact, one reason for using them is to

figure out whether the priors you came up

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with results in sensible ranges of

possible parameter estimates, right?

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In some cases, especially with these

complex multivariate models, your priors

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may interact in unexpected ways and then

result in predictions that are not in line

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with what your theory is actually telling

you you should expect.

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And so prior predictive checks basically

until you specify your priors for all your

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parameters.

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And then you generate

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parameter values from those priors by

combining it with your model

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specification.

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And then those combinations of parameter

estimates are used to generate what are

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called prior predictive samples.

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So these are samples of some pre

-specified size that represent possible

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observations that align with what your

priors are conveying combined with your

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model.

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And so ideally,

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those prior predictive samples look kind

of like what you would expect your data to

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look like.

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And sometimes for researchers, it is

easier to think about what the data should

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look like compared to what the parameter

estimates can be.

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And so in that sense, prior predictive

checks can be really helpful in checking

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not just the priors, but checking the

researcher and making sure that they

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actually convey their knowledge to me, for

example, correctly.

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Yeah, did that answer your question?

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Yeah, yeah, I think that's a great

definition and definitely encourage any

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Bayesian practitioner to include prior

predictive checks in their workflow.

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Once you have written a model, that should

be the first thing you do.

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Do not run a CMC before doing prior

predictive checks.

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And recently, I feel like a lot of the

software packages for Bayesian methods

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have...

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included very simple ways of running these

checks, which when I first started looking

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at them, it was kind of more of a niche

step in the workflow.

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And so it required a few more steps and

some more like coding, but now it's as

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easy as just switching like a toggle to

get those prior predictive samples.

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So that's great.

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Yeah, yeah, yeah, completely agree.

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That's also, yeah, it's definitely

something that's, that's been more and

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more popular in the different

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classes and courses that I teach, whether

it's online courses or live workshops,

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always show prior predictive checks almost

all the time.

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So yeah, it's becoming way, way more

popular and widespread.

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So that's really good because I can tell

you when I work on a real model for

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clients, always the first thing I do

before running MCMC is prior predictive

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checks.

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And actually there is a fantastic way

of...

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you know, doing prior predictive checks,

like kind of industrialized and that's

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called simulation based calibration.

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Have you heard of that?

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No, I mean, maybe the term, but I have no

idea what it is.

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So that's just like making prior

predictive checks on an industrialized

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scale.

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Basically now instead of just

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running through the model forward, as you

explained, and generate prior predictive

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samples, what you're doing with SPC, so

simulation -based calibration, is

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generating not only prior predictive

samples, but prior samples of the

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parameters of the model.

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You stock these parameters in some object.

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but you don't give them to the model, but

you keep them somewhere safe.

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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.

:

01:04:36,493 --> 01:04:43,353

I wanted to be a vet or something, but

then I had to take my pets to the vet and

:

01:04:43,353 --> 01:04:44,013

they were

:

01:04:44,013 --> 01:04:47,493

bleeding and I was like, no, I don't want

the event anymore.

:

01:04:48,293 --> 01:04:56,733

Well, it depends on the kind of animals

you treat, but veterinarian can be a

:

01:04:56,733 --> 01:05:00,053

thrill seeking experience too.

:

01:05:00,053 --> 01:05:07,513

You know, like if you're specialized in

snakes or grizzlies or lions, I'm guessing

:

01:05:07,513 --> 01:05:12,827

it's not all the time, you know, super,

super easy and tranquil.

:

01:05:13,645 --> 01:05:14,825

no.

:

01:05:16,545 --> 01:05:17,005

Awesome.

:

01:05:17,005 --> 01:05:19,865

Well Sonia, that was really great to have

you on the show.

:

01:05:19,865 --> 01:05:22,285

Of course, I'm going to ask you the last

two questions.

:

01:05:22,285 --> 01:05:24,625

Ask every guest at the end of the show.

:

01:05:24,625 --> 01:05:29,725

So if you had unlimited time and

resources, which problem would you try to

:

01:05:29,725 --> 01:05:30,341

solve?

:

01:05:32,045 --> 01:05:37,185

I thought about this a lot because I

wanted to solve many problems.

:

01:05:37,525 --> 01:05:41,805

So when I give this answer, I'm hoping

that other people are taking care of all

:

01:05:41,805 --> 01:05:43,005

those other problems.

:

01:05:43,005 --> 01:05:48,505

But I think something that I've noticed

recently is that a lot of people seem to

:

01:05:48,505 --> 01:05:56,505

have lost the ability or the interest in

critical thinking and being curious and

:

01:05:56,505 --> 01:05:59,245

trying to figure out things by yourself.

:

01:05:59,245 --> 01:06:02,093

And so that's something that I would like

to.

:

01:06:02,093 --> 01:06:04,533

solve or improve somehow?

:

01:06:04,533 --> 01:06:10,193

Don't ask me how, but I think being a

critical thinker and being curious are two

:

01:06:10,193 --> 01:06:17,173

really important skills to have to succeed

in our society right now.

:

01:06:17,173 --> 01:06:23,513

I mean, there's so much information being

thrown at us that it's really up to you to

:

01:06:23,513 --> 01:06:26,633

figure out what to focus on and what to

ignore.

:

01:06:26,633 --> 01:06:30,061

And for that, you really need this

critical thinking skill and...

:

01:06:30,061 --> 01:06:33,461

and also the curiosity to actually look

for information.

:

01:06:33,461 --> 01:06:38,681

And so I think that's, it's also a very

educational problem, I feel.

:

01:06:38,681 --> 01:06:43,161

So if it's where I am right now in my

career, but yeah, that would be something

:

01:06:43,161 --> 01:06:44,521

to solve.

:

01:06:44,641 --> 01:06:45,601

Yeah.

:

01:06:45,861 --> 01:06:49,181

Completely understand that was actually my

answer also.

:

01:06:49,181 --> 01:06:50,511

So I like, really?

:

01:06:50,511 --> 01:06:51,261

Yeah.

:

01:06:51,261 --> 01:06:51,641

Yeah.

:

01:06:51,641 --> 01:06:51,921

Yeah.

:

01:06:51,921 --> 01:06:53,261

I completely agree with you.

:

01:06:53,261 --> 01:06:53,621

Yeah.

:

01:06:53,621 --> 01:06:55,041

These are topics I found.

:

01:06:55,041 --> 01:06:56,161

I find them.

:

01:06:56,161 --> 01:06:57,241

I find super interesting.

:

01:06:57,241 --> 01:06:58,181

How do you.

:

01:06:58,221 --> 01:07:02,581

do we teach critical thinking, how do we

teach the scientific methods, things like

:

01:07:02,581 --> 01:07:02,821

that.

:

01:07:02,821 --> 01:07:07,401

It's always something I'm super excited to

talk about.

:

01:07:07,561 --> 01:07:13,941

Yeah, I also hope it will have some sort

of trickle down effect on all the other

:

01:07:13,941 --> 01:07:14,721

problems, right?

:

01:07:14,721 --> 01:07:18,661

Once the whole world is very skilled at

critical thinking, all the other issues

:

01:07:18,661 --> 01:07:22,001

will be resolved pretty quickly.

:

01:07:22,101 --> 01:07:27,149

Yeah, not only because it's directly

solved, but...

:

01:07:27,149 --> 01:07:34,729

I would say mainly because then you have

maybe less barriers.

:

01:07:35,809 --> 01:07:39,789

And so yeah, probably coming from that.

:

01:07:40,429 --> 01:07:46,709

And then second question, if you could

have dinner with any great scientific

:

01:07:46,709 --> 01:07:50,869

mind, dead, alive or fictional food.

:

01:07:51,929 --> 01:07:54,285

So I ended up

:

01:07:54,285 --> 01:07:59,485

Choosing Ada Lovelace who's like one of

the first or maybe the first woman who

:

01:07:59,485 --> 01:08:02,525

ever worked in computer programming area.

:

01:08:02,525 --> 01:08:06,785

I think she's very interesting I also

recently found out that she passed away

:

01:08:06,785 --> 01:08:12,505

when she was only like 36 Which is like

I'm I'm getting at that age and she

:

01:08:12,505 --> 01:08:16,665

already accomplished all these things By

the time she passed away and so now I'm

:

01:08:16,665 --> 01:08:22,145

like, okay I gotta I gotta step it up, but

I would really love to talk to her about

:

01:08:22,145 --> 01:08:24,027

just her experience.

:

01:08:24,077 --> 01:08:30,657

being so unique in that very manly world

and in that very manly time in general, I

:

01:08:30,657 --> 01:08:36,017

think it would be very interesting to hear

the challenges and also maybe some

:

01:08:36,017 --> 01:08:40,577

advantages or like benefits that she saw,

like why did she go through all this

:

01:08:40,577 --> 01:08:42,597

trouble to begin with?

:

01:08:42,597 --> 01:08:47,237

Yeah, I think it would be an interesting

conversation to have for sure.

:

01:08:48,017 --> 01:08:49,757

Yeah, yeah, definitely.

:

01:08:49,757 --> 01:08:50,757

Yeah, great choice.

:

01:08:50,757 --> 01:08:53,549

I think, I think somebody already

:

01:08:53,549 --> 01:08:54,289

had answered.

:

01:08:54,289 --> 01:08:59,269

I don't remember who, but yeah, it's not a

very common choice.

:

01:08:59,269 --> 01:09:02,709

We can have a dinner party together.

:

01:09:03,049 --> 01:09:04,129

Yeah, exactly.

:

01:09:04,129 --> 01:09:05,329

That's perfect.

:

01:09:05,449 --> 01:09:06,649

Fantastic.

:

01:09:06,929 --> 01:09:07,689

Great.

:

01:09:07,689 --> 01:09:08,289

Thank you.

:

01:09:08,289 --> 01:09:09,989

Thank you so much, Sonja.

:

01:09:09,989 --> 01:09:11,829

That was a blast.

:

01:09:11,889 --> 01:09:13,889

I learned so much.

:

01:09:14,609 --> 01:09:15,909

Me too.

:

01:09:16,509 --> 01:09:18,049

You're welcome.

:

01:09:18,849 --> 01:09:23,245

And well, as usual, I put resources and a

link to a website.

:

01:09:23,245 --> 01:09:26,685

in the show notes for those who want to

dig deeper.

:

01:09:26,685 --> 01:09:30,165

Thank you again, Sonia, for taking the

time and being on this show.

:

01:09:30,465 --> 01:09:31,765

Yeah, thank you.

:

01:09:31,765 --> 01:09:33,701

It was so much fun.

:

01:09:37,869 --> 01:09:41,609

This has been another episode of Learning

Bayesian Statistics.

:

01:09:41,609 --> 01:09:46,569

Be sure to rate, review, and follow the

show on your favorite podcatcher, and

:

01:09:46,569 --> 01:09:51,489

visit learnbaystats .com for more

resources about today's topics, as well as

:

01:09:51,489 --> 01:09:56,229

access to more episodes to help you reach

true Bayesian state of mind.

:

01:09:56,229 --> 01:09:58,149

That's learnbaystats .com.

:

01:09:58,149 --> 01:10:02,989

Our theme music is Good Bayesian by Baba

Brinkman, fit MC Lass and Meghiraam.

:

01:10:02,989 --> 01:10:06,149

Check out his awesome work at bababrinkman

.com.

:

01:10:06,149 --> 01:10:07,309

I'm your host.

:

01:10:07,309 --> 01:10:08,289

Alex Andorra.

:

01:10:08,289 --> 01:10:12,549

You can follow me on Twitter at Alex

underscore Andorra, like the country.

:

01:10:12,549 --> 01:10:17,629

You can support the show and unlock

exclusive benefits by visiting Patreon

:

01:10:17,629 --> 01:10:19,809

.com slash LearnBasedDance.

:

01:10:19,809 --> 01:10:22,249

Thank you so much for listening and for

your support.

:

01:10:22,249 --> 01:10:24,489

You're truly a good Bayesian.

:

01:10:24,489 --> 01:10:28,039

Change your predictions after taking

information in.

:

01:10:28,039 --> 01:10:34,149

And if you're thinking I'll be less than

amazing, let's adjust those expectations.

:

01:10:34,605 --> 01:10:40,065

Let me show you how to be a good Bayesian

Change calculations after taking fresh

:

01:10:40,065 --> 01:10:46,045

data in Those predictions that your brain

is making Let's get them on a solid

:

01:10:46,045 --> 01:10:47,845

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