Bayesian Multiple Testing Using Student’s T-Distribution

• Activity Number: 613 - Robust Learning and Posterior Summary
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): G. M. Nilupika Kumari Herath* and Siva Sivaganesan
• Companies: Department of Mathematical Sciences, University of Cincinnati,Ohio 45221 and University of Cincinnati
• Keywords: Multiple comparisons; Student’s t-distribution; hierarchical modeling; importance sampling; Markov chain Monte Carlo (MCMC)

Abstract

Literature on multiple testing and multiplicity adjustment with continuous response variables mostly focus on normally distributed responses. The normality assumption may be too restrictive in some cases, e.g. it has been shown that 5 to 15 % of the DNA samples deviate from normality and very close to t-distribution. It would be of interest to study the sensitivity of normality assumption when the response variables instead follow a t-distribution. We focus on Bayesian multiple testing of means, or location parameters, when the response variable follows a t-distributions, determine suitable priors for the parameters, develop a computational strategy for computing the posterior probabilities of the hypotheses, and use it study the sensitivity of the results under normality assumption using simulation study. While the results for strong signals under both t and normal distribution assumptions are very similar, they differ for moderate and weak signals.