2014/02/15 by Lucien Birgé, Birgé, Lucien
Decision Sciences · Mathematics · #62F05 (Primary) #62G15 (Secondary) #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62F05 #msc:62G15 #stat.TH
paper · pdf · doi:10.48550/arxiv.1402.3695
Extended version of a talk given in June 2013 at BNP9 Conference in Amsterdam - 17 pages
openalex publication_date 2014/02/15 · arxiv created 2014/10/31 · arxiv updated 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates the \em nonasymptotic properties of Bayes procedures for estimating an unknown distribution from n i.i.d. observations. We assume that the prior is supported by a model (\scrS,h) (where h denotes the Hellinger distance) with suitable metric properties involving the number of small balls that are needed to cover larger ones. We also require that the prior put enough probability on small balls. We consider two different situations. The simplest case is the one of a parametric model containing the target density for which we show that the posterior concentrates around the true distribution at rate 1/√(n). In the general situation, we relax the parametric assumption and take into account a possible mispecification of the model. Provided that the Kullback-Leibler Information between the true distribution and \scrS is finite, we establish risk bounds for the Bayes estimators.