Objective Bayesian multiple comparisons between two normal models with unequal variances

초록

This paper explores objective Bayesian multiple hypothesis testing within the context of normal models with heterogeneous variances. To address the computational challenges associated with Bayesian multiple testing, particularly as the number of hypotheses increases, we propose novel objective Bayesian procedures that significantly reduce computational burden. Our approach involves ranking null hypotheses based on their Bayes factors, followed by the identification and evaluation of feasible configurations of true and false null hypotheses. We employ an objective Bayesian framework that incorporates underlying non-nested models, either through a comprehensive model encompassing all alternative hypotheses or by integrating the null model into any other model. This approach effectively reduces the number of models under consideration from 2^k to k+1, where k is the number of null hypotheses. We demonstrate the consistency of our proposed procedures and evaluate their performance using both simulated and real-world datasets.

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