Asymptotic theory of dependent Bayesian multiple testing procedures under possible model misspecification

• Published in: Annals of the Institute of Statistical Mathematics Vol. 73; no. 5; pp. 891 - 920
• Main Authors: Chandra, Noirrit Kiran, Bhattacharya, Sourabh
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 01.10.2021; Springer Nature B.V
• Subjects: Asymptotic methods; Asymptotic properties; Bayesian analysis; Economics; Error analysis; Finance; Insurance; Management; Mathematics; Mathematics and Statistics; Statistics; Statistics for Business; Test procedures; False discovery rate; Posterior convergence; Misspecified model; Bayesian multiple testing; Kullback–Leibler; Variable selection
• ISSN: 0020-3157; 1572-9052
• DOI: 10.1007/s10463-020-00770-3

We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated error measures that coherently accounts for the dependence structure present in the model. We advocate posterior versions of FDR and FNR as appropriate error rates and show that their asymptotic convergence rates are directly associated with the Kullback–Leibler divergence from the true model. The theories hold regardless of the class of postulated models being misspecified. We illustrate our results in a variable selection problem with autoregressive response variables and compare our procedure with some existing methods through simulation studies. Superior performance of the new procedure compared to the others indicates that proper exploitation of the dependence structure by multiple testing methods is indeed important. Moreover, we obtain encouraging results in a maize dataset, where we select influential marker variables.