Bayesian theory in modern statistics and data science

Seminar in Mathematics

Abstract: Bayesian methods have flourished in modern statistics and machine learning due to a number of attractive properties, including their interpretability, ability to incorporate prior knowledge or physical constraints, and since they provide uncertainty quantification amongst other things. Their contemporary use has resulted in methodological and computational innovations, which have in turn led to the need for new theory to understand whether the outputs from such Bayesian algorithms are statistically reliable. I will discuss some current uses of Bayesian methods, and how the interplay of theory and methodology can play a meaningful role in analyzing and improving their performance. This will be illustrated via examples related to my recent research, for instance in inverse problems, inference for stochastic processes and variational inference.