On a New Class of Multivariate Prior Distributions: Theory and Application in Reliability

Abstract

In the context of robust Bayesian analysis for multiparameter distributions, we introduce a new class of priors based on stochastic orders, multivariate total positivity of order 2 ($MT{P}_2$) and weighted distributions. We provide the new definition, its interpretation and the main properties and we also study the relationship with other classical classes of prior beliefs. We also consider the Hellinger metric and the Kullback-Leibler divergence to measure the uncertainty induced by such a class, as well as its effect on the posterior distribution. Finally, we conclude the paper with a real example about train door reliability.