The Development of Bayesian Statistics

Abstract

The incorporation of Bayesian inference into practical statistics has seen many changes over the past century, including hierarchical and nonparametric models, general computing tools that have allowed the routine use of nonconjugate distributions, and the incorporation of model checking and validation in an iterative process of data analysis. We discuss these and other technical advances along with parallel developments in philosophy, moving beyond traditional subjectivist and objectivist frameworks to ideas based on prediction and falsifcation. Bayesian statistics is a fexible and powerful approach to applied statistics and an imperfect but valuable way of understanding statistics more generally.