2004/05/27 by James O. Berger, Luis R. Pericchi
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Statistical Methods and Bayesian Inference #math.ST #msc:62B10 #msc:62F03 #msc:62F15 #msc:62F40. #msc:62N03 #stat.TH
paper · pdf · doi:10.1214/009053604000000229
published as Annals of Statistics 2004, Vol. 32, No. 3, 841-869
openalex publication_date 2004/05/27 · arxiv created 2004/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal training samples. When data can vary widely in terms of either information content or impact on the improper priors, use of minimal training samples can be inadequate. Important examples include certain cases of discrete data, the presence of censored observations, and certain situations involving linear models and explanatory variables. Such situations require more sophisticated methods of choosing training samples. A variety of such methods are developed in this paper, and successfully applied in challenging situations.