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The influence of misspecified covariance on false discovery control when using posterior probabilities

ABSTRACT This paper focuses on the influence of a misspecified covariance structure on false discovery rate for the large-scale multiple testing problem. Specifically, we evaluate the influence on the marginal 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 marginal distributions under both correctly specified and incorrectly specified models are derived. The Kullback–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 on soil humidity is discussed.