The influence of misspecified covariance on false discovery control when usingposterior probabilities

This paper focuses on the influence of a misspecified covariance structure on false discoveryrate for the large-scale multiple testing problem.Specifically,we evaluate the influence on themarginal distribution of local false discovery rate statistics,which are used in many multiple testing procedures and related to Bayesian posterior probabilities.Explicit forms of the marginaldistributions under both correctly specified and incorrectly specified models are derived.TheKullback–Leibler divergence is used to quantify the influence caused by a misspecification.Several numerical examples are provided to illustrate the influence.A real spatio-temporal data onsoil humidity is discussed.