Objective Bayesian inference for stress-strength models and Bayesian ANOVA

Abstract

First of all, for estimating the reliabilities in Weibull stress-strength models, some matching priors are derived based on a modi ed pro le likelihood. Simulation studies show that these matching priors perform well with small sample sizes. Next, a generalized Zellner's g-prior is proposed for model selection in linear models with grouped covariates. The marginal likelihood function and a simple closed form of it are derived. The issue of computing the Bayes factors is addressed, and the performance of the Bayes factors is examined by numerical studies. Finally, the Bayes factors under the proposed prior in some 2-way ANOVA models are proved to be consistent.