On rates of convergence for posterior distributions in infinite-dimensional models

TL;DR

This paper presents a new method for analyzing how quickly Bayesian posterior distributions converge in infinite-dimensional models, improving existing convergence rate results for certain complex models.

Contribution

It extends recent Bayesian consistency approaches to derive faster convergence rates for models like Dirichlet process mixtures and Bernstein polynomials.

Findings

Improved convergence rates for Dirichlet process mixture models

Enhanced rates for Bernstein polynomial models

A novel framework for studying posterior convergence

Abstract

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of convergence for models including the mixture of Dirichlet process model and the random Bernstein polynomial model.