Zero-Sum Constraints Enhance Sampling

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Takeaways:

• Zero Sum constraints allow for better sampling and estimation in hierarchical models.
• Understanding the difference between population and sample means is crucial.
• A library for zero-sum normal effects would be beneficial.
• Practical solutions can yield decent predictions even with limitations.
• Cholesky parameterization can be adapted for positive correlation matrices.
• Understanding the geometry of sampling spaces is crucial.
• The relationship between eigenvalues and sampling is complex.
• Collaboration and sharing knowledge enhance research outcomes.
• Innovative approaches can simplify complex statistical problems.

Chapters:

03:35 Sean Pinkney's Journey to Bayesian Modeling

11:21 The Zero-Sum Normal Project Explained

18:52 Technical Insights on Zero-Sum Constraints

32:04 Handling New Elements in Bayesian Models

36:19 Understanding Population Parameters and Predictions

49:11 Exploring Flexible Cholesky Parameterization

01:07:23 Closing Thoughts and Future Directions

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, Francesco Madrisotti, Ivy Huang, Gary Clarke, Robert Flannery, Rasmus Hindström, Stefan, Corey Abshire, Mike Loncaric, David McCormick, Ronald Legere, Sergio Dolia, Michael Cao, Yiğit Aşık and Suyog Chandramouli.

Links from the show:

• Sean's website: https://spinkney.github.io/
• Sean on LinkedIn: https://www.linkedin.com/in/sean-pinkney123/
• Sean on GitHub: https://github.com/spinkney
• Sean on BlueSky: https://bsky.app/profile/spinkney.bsky.social
• Sean on Mastodon: https://fosstodon.org/@spinkney
• Sean's talk at StanCon 2024: https://youtu.be/eE8Vqxs8OfQ?si=09-vNvCxpbz8enUj
• Flexible Cholesky Parameterization of Correlation Matrices: https://arxiv.org/abs/2405.07286
• Quantile Regressions in Stan: https://spinkney.github.io/posts/post-2-quantile-reg-series/post-2-quantile-reg-part-I/quantile-reg.html
• LBS #74 Optimizing NUTS and Developing the ZeroSumNormal Distribution, with Adrian Seyboldt: https://learnbayesstats.com/episode/74-optimizing-nuts-developing-zerosumnormal-distribution-adrian-seyboldt

Transcript

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