Bayesian methods for generalized linear models with covariates missing at random

The authors propose methods for Bayesian inference for generalized linear models with missing covariate data. They specify a parametric distribution for the covariates that is written as a sequence of one-dimensional conditional distributions. They propose an informative class of joint prior distributions for the regression coefficients and the parameters arising from the covariate distributions. They examine the properties of the proposed prior and resulting posterior distributions. They also present a Bayesian criterion for comparing various models, and a calibration is derived for it. A detailed simulation is conducted and two real data sets are examined to demonstrate the methodology. Methodes bayesiennes pour modeles lineaires generalises dont certaines valeurs des covariables sont manquantes de facon fortuite Les auteurs proposent des methodes d'inference bayesienne adaptees aux modeles lineaires gene-ralises pour les situations ou les valeurs de certaines covariables sont manquantes au hasard. La loi parametrique choisie pour les covariables s'exprime comme succession de lois conditionnelles univariees. Une classe de lois a priori informative est suggeree pour les coefficients de regression et pour les parametres lies aux lois des covariables. Les auteurs examinent les proprietes de ces lois a priori et des lois a posteriori qui en decoulent. Ils presentent aussi un critere bayesien pour la comparaison des differents modeles et montrent comment le calibrer. Une simulation detaillee et l'examen de deux ensembles de donnees reelles illustrent l'approche proposee.

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