This is a course on advanced Bayesian inference in the context of contemporary data applications.
It is designed to equip students with both deep theoretical foundations as well as practical tools for modern Bayesian analysis.
Its primary objectives are to:
- Build intuition and confidence in using priors with emphasis on prior calibration,
- Gain a solid understanding of the core principles underlying Bayesian decision theory,
- Explore the theoretical foundations connecting frequentist and Bayesian perspectives,
- Engage with, and develop mastery of, Bayesian nonparametric theory and methods,
- Learn to implement modern (generative) posterior inference techniques,
- Build proficiency in analyzing and interpreting large-scale datasets using Bayesian methods.
This course captures the essence of being Bayesian in the 21st century, tracing the evolution of Bayesian thought from its theoretical foundations to modern developments such as generative Bayes. The goal of this course is not to dwell on dry proofs written on a board, but to cultivate intuition and a deep appreciation for the Bayesian approach to thinking and decision making. It blends theory, methodology, computation and hands-on practice. Embracing the Bayesian perspective often demands thoughtful, and sometimes uncompromising, choices of priors and likelihoods.
Throughout the course, we will explore key principles that underpin or alleviate such choices towards meaningful and theoretically sound Bayesian data analysis.
Lectures will emphasize methodology, computation and theory but will also feature several real datasets. The goals is not to provide a compendium of techniques but rather to create links between various approaches and to explore their applicability in real life.
The curriculum begins with traditional (parametric) Bayesian statistics and progressively advances through nonparametric priors, likelihood-free inference, and prediction-driven inference, culminating in some of the most cutting-edge research-driven creative developments in Bayes.
Topics include Bayesian decision theory, Bayesian sparsity, Bayesian machine learning and nonparametrics, likelihood-free inference, generative Bayesian models, or variational and predictive inference.
By the end of the course, students will be be able to confidently apply Bayesian tools in realworld settings and will have developed the theoretical and methodological foundation necessary to pursue both applied and methods–oriented research.
