Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.
Accepté le :
DOI : 10.1051/ps/2018023
Mots-clés : Incompatibility, conditional distribution, Markov kernel, optimal compromise, Kriging, reference prior, integrated likelihood, Gibbs sampling, posterior propriety, frequentist coverage
@article{PS_2019__23__271_0,
author = {Mur\'e, Joseph},
title = {Optimal compromise between incompatible conditional probability distributions, with application to {Objective} {Bayesian} {Kriging}},
journal = {ESAIM: Probability and Statistics},
pages = {271--309},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018023},
mrnumber = {3963529},
zbl = {1420.62117},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2018023/}
}
TY - JOUR AU - Muré, Joseph TI - Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging JO - ESAIM: Probability and Statistics PY - 2019 SP - 271 EP - 309 VL - 23 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2018023/ DO - 10.1051/ps/2018023 LA - en ID - PS_2019__23__271_0 ER -
%0 Journal Article %A Muré, Joseph %T Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging %J ESAIM: Probability and Statistics %D 2019 %P 271-309 %V 23 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2018023/ %R 10.1051/ps/2018023 %G en %F PS_2019__23__271_0
Muré, Joseph. Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 271-309. doi : 10.1051/ps/2018023. http://www.numdam.org/articles/10.1051/ps/2018023/
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