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

2007/04/01 by Stephen G. Walker, Antonio Lijoi, Igor Prünster · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #math.ST #msc:62F15 #msc:62G07 #msc:62G20 #stat.TH

paper · pdf · doi:10.1214/009053606000001361

published as Annals of Statistics 2007, Vol. 35, No. 2, 738-746 · Published at http://dx.doi.org/10.1214/009053606000001361 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2007/04/01 · arxiv created 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Bayesian Density Estimation and Inference Using Mixtures

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• Borrowing strengh in hierarchical Bayes: Posterior concentration of the Dirichlet base measure