Compatibility results for conditional distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:125

Article

Berti, Patrizia¹  Dreassi, Emanuela²  Rigo, Pietro³ 

[1] Univ Modena & Reggio Emilia, Dipartimento Matemat Pura & Applicata G Vitali, I-41100 Modena, Italy

[2] Univ Firenze, Dipartimento Stat Informat Applicaz G Parenti, I-50134 Florence, Italy

[3] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

关键词: Bayesian inference;    Compatibility of conditional distributions;    Exchangeability;    Gibbs sampling;    Markov random fields;    Multiple imputation;   

DOI  :  10.1016/j.jmva.2013.12.009

来源: Elsevier

【 摘 要 】

In various frameworks, to assess the joint distribution of a k-dimensional random vector X = (X-1, ... , X-k), one selects some putative conditional distributions Q(1), ... , Q(k). Each Q(i) is regarded as a possible (or putative) conditional distribution for X-i given (X-1, ... , Xi-1, Xi+1, ... , X-k). The Q(i) are compatible if there is a joint distribution P for X with conditionals Q1, ... , Q(k). Three types of compatibility results are given in this paper. First, the X-i are assumed to take values in compact subsets of R. Second, the Q(i) are supposed to have densities with respect to reference measures. Third, a stronger form of compatibility is investigated. The law P with conditionals Q(1), ... , Q(k) is requested to belong to some given class P-0 of distributions. Two choices for P-0 are considered, that is, P-0 = (exchangeable laws} and P-0 = {laws with identical univariate marginals}. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free