Emerging Directions in Bayesian Computation

Abstract

Bayesian models are powerful tools for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty through the posterior distribution. Practical posterior computation is commonly performed via MCMC, which can be computationally infeasible for high-dimensional models with many observations. In this article, we discuss the potential to improve posterior computation using ideas from machine learning. Concrete directions are explored in vignettes on normalizing flows, statistical properties of variational approximations, Bayesian coresets and distributed Bayesian inference.