Exploring Bayesian Statistics and Gaussian Processes

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• My Intuitive Bayes Online Courses
• 1:1 Mentorship with me

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work!

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Takeaways:

• Bayesian statistics is a powerful framework for handling complex problems, making use of prior knowledge, and excelling with limited data.
• Bayesian statistics provides a framework for updating beliefs and making predictions based on prior knowledge and observed data.
• Bayesian methods allow for the explicit incorporation of prior assumptions, which can provide structure and improve the reliability of the analysis.
• There are several Bayesian frameworks available, such as PyMC, Stan, and Bambi, each with its own strengths and features.
• PyMC is a powerful library for Bayesian modeling that allows for flexible and efficient computation.
• For beginners, it is recommended to start with introductory courses or resources that provide a step-by-step approach to learning Bayesian statistics.
• PyTensor leverages GPU acceleration and complex graph optimizations to improve the performance and scalability of Bayesian models.
• ArviZ is a library for post-modeling workflows in Bayesian statistics, providing tools for model diagnostics and result visualization.
• Gaussian processes are versatile non-parametric models that can be used for spatial and temporal data analysis in Bayesian statistics.

Chapters:

00:00 Introduction to Bayesian Statistics

07:32 Advantages of Bayesian Methods

16:22 Incorporating Priors in Models

23:26 Modeling Causal Relationships

30:03 Introduction to PyMC, Stan, and Bambi

34:30 Choosing the Right Bayesian Framework

39:20 Getting Started with Bayesian Statistics

44:39 Understanding Bayesian Statistics and PyMC

49:01 Leveraging PyTensor for Improved Performance and Scalability

01:02:37 Exploring Post-Modeling Workflows with ArviZ

01:08:30 The Power of Gaussian Processes in Bayesian Modeling

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:

• Original episode on the Super Data Science podcast: https://www.superdatascience.com/podcast/bayesian-methods-and-applications-with-alexandre-andorra
• Advanced Regression with Bambi and PyMC: https://www.intuitivebayes.com/advanced-regression
• Gaussian Processes: HSGP Reference & First Steps: https://www.pymc.io/projects/examples/en/latest/gaussian_processes/HSGP-Basic.html
• Modeling Webinar – Fast & Efficient Gaussian Processes: https://www.youtube.com/watch?v=9tDMouGue8g
• Modeling spatial data with Gaussian processes in PyMC: https://www.pymc-labs.com/blog-posts/spatial-gaussian-process-01/
• Hierarchical Bayesian Modeling of Survey Data with Post-stratification: https://www.pymc-labs.com/blog-posts/2022-12-08-Salk/
• PyMC docs: https://www.pymc.io/welcome.html
• Bambi docs: https://bambinos.github.io/bambi/
• PyMC Labs: https://www.pymc-labs.com/
• LBS #50 Ta(l)king Risks & Embracing Uncertainty, with David Spiegelhalter: https://learnbayesstats.com/episode/50-talking-risks-embracing-uncertainty-david-spiegelhalter/
• LBS #51 Bernoulli’s Fallacy & the Crisis of Modern Science, with Aubrey Clayton: https://learnbayesstats.com/episode/51-bernoullis-fallacy-crisis-modern-science-aubrey-clayton/
• LBS #63 Media Mix Models & Bayes for Marketing, with Luciano Paz: https://learnbayesstats.com/episode/63-media-mix-models-bayes-marketing-luciano-paz/
• LBS #83 Multilevel Regression, Post-Stratification & Electoral Dynamics, with Tarmo Jüristo: https://learnbayesstats.com/episode/83-multilevel-regression-post-stratification-electoral-dynamics-tarmo-juristo/
• Jon Krohn on YouTube: https://www.youtube.com/JonKrohnLearns
• Jon Krohn on Linkedin: https://www.linkedin.com/in/jonkrohn/
• Jon Krohn on Twitter: https://x.com/JonKrohnLearns

Transcript

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