2016/11/04 by Noirrit Kiran Chandra, Chandra, Noirrit K., Sourabh Bhattacharya +1
Mathematics · #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1611.01369
openalex publication_date 2016/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study asymptotic properties of Bayesian multiple testing procedures and\nprovide sufficient conditions for strong consistency under general dependence\nstructure. We also consider a novel Bayesian multiple testing procedure and\nassociated error measures that coherently accounts for the dependence structure\npresent in the model. We advocate posterior versions of FDR and FNR as\nappropriate error rates and show that their asymptotic convergence rates are\ndirectly associated with the Kullback-Leibler divergence from the true model.\nOur results hold even when the class of postulated models is misspecified. We\nillustrate our results in a variable selection problem with autoregressive\nresponse variables, and compare the new Bayesian procedure with some existing\nmethods through extensive simulation studies in the variable selection problem.\nSuperior performance of the new procedure compared to the others vindicate that\nproper exploitation of the dependence structure by multiple testing methods is\nindeed important. Moreover, we obtain encouraging results in a real, maize data\ncontext, where we select influential marker variables.\n