Convergence rates for posterior distributions and adaptive estimation

2004/08/01 by Tzee‐Ming Huang, Tzee-Ming Huang · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #msc:62A15 #msc:62G07. #msc:62G20 #stat.TH

paper · pdf · doi:10.1214/009053604000000490

published as Annals of Statistics 2004, Vol. 32, No. 4, 1556-1593 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000490

openalex publication_date 2004/08/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.

Citations

• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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