#109 Prior Sensitivity Analysis, Overfitting & Model Selection, with Sonja Winter
Learning Bayesian Statistics
Innovations in Bayesian Calibration
This chapter explores the intricacies and applications of Bayesian models, particularly in educational research and structural equation modeling. It emphasizes the efficiency of amortized Bayesian inference and addresses challenges related to missing data and small sample sizes. The speakers highlight the potential of Bayesian methods to provide deeper insights into complex data structures and inform policy decisions effectively.
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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!
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
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