2020/04/30 by Noirrit Kiran Chandra, Chandra, Noirrit Kiran, 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.2005.00066
openalex publication_date 2020/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we investigate the asymptotic properties of Bayesian\nmultiple testing procedures under general dependent setup, when the sample size\nand the number of hypotheses both tend to infinity. Specifically, we\ninvestigate strong consistency of the procedures and asymptotic properties of\ndifferent versions of false discovery and false non-discovery rates under the\nhigh dimensional setup. We particularly focus on a novel Bayesian non-marginal\nmultiple testing procedure and its associated error rates in this regard. Our\nresults show that the asymptotic convergence rates of the error rates are\ndirectly associated with the Kullback-Leibler divergence from the true model,\nand the results hold even when the postulated class of models is misspecified.\nFor illustration of our high-dimensional asymptotic theory, we consider a\nBayesian variable selection problem in a time-varying covariate selection\nframework, with autoregressive response variables. We particularly focus on the\nsetup where the number of hypotheses increases at a faster rate compared to the\nsample size, which is the so-called ultra-high dimensional situation.\n