The Inuence of Misspecified Covariance on False Discovery Control when Using Posterior Probabilities

TL;DR

This paper investigates how misspecifying the covariance structure affects false discovery rate control in large-scale multiple testing, especially through the lens of local false discovery rates and Bayesian posterior probabilities.

Contribution

It derives explicit forms of marginal distributions under correct and incorrect models and quantifies the impact of misspecification using Kullback-Leibler divergence.

Findings

Misspecification significantly alters local fdr distributions.

Explicit formulas help understand the impact of covariance misspecification.

Numerical examples and a real data case illustrate the effects.

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 fdr 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.