On convergence rates of Bayesian predictive densities and posterior distributions

TL;DR

This paper analyzes the convergence rates of Bayesian predictive densities and posterior distributions across various data settings, emphasizing a unified approach for large-sample properties in nonparametric Bayesian analysis.

Contribution

It introduces a unified analytical framework for Bayesian asymptotics based on predictive densities applicable to multiple data dependence structures.

Findings

Provides convergence rate results for Bayesian posterior distributions

Unifies analysis across iid, mis-specified, non-iid, and dependent data

Enhances understanding of Bayesian large-sample properties

Abstract

Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics based primarily on predictive densities. Our analysis is unified in the sense that essentially the same approach can be taken to develop convergence rate results in iid, mis-specified iid, independent non-iid, and dependent data cases.