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.

Keywords:

• Multiple testing
• Bayes
• dependent data
• divergence
• spatio-temporal

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is partially supported by National Science Foundation [grant number OIA-1301789].

Notes on contributors

Ye Liang

Ye Liang is an assistant professor in the Department of Statistics at Oklahoma State University, USA. His research areas include Bayesian statistics and spatial statistics. He primarily focuses on applications in ecological, agricultural and environmental studies, and biomedical and healthcare studies.

Joshua D. Habiger

Joshua D. Habiger is an associate professor in the Department of Statistics at Oklahoma State University, USA. His research interests include high dimensional statistical inference and categorical data analysis.

Xiaoyi Min

Xiaoyi Min is an assistant professor in the Department of Mathematics and Statistics at Georgia State University. His research interests include Bayesian statistics, statistical genetics and meta-analysis.