Title: An Introduction to Bayesian Hypothesis Testing for ANOVA Designs
Abstract: In this talk, we explore Bayesian approaches for the hypothesis testing problem in multiway analysis-of-variance (ANOVA) models. We first specialize the result in a two-sample scenario as an intermediate step toward developing the Bayes factors for ANOVA designs. Given that the design matrix is not necessarily of full rank, we adopt the sum-to-zero constraint for uniqueness and employ the singular value decomposition (SVD) method to reparameterize the model to get rid of the additional constraint. We then derive the Bayes factors under a class of Zellner’s g-priors. In particular, we examine asymptotic properties of the proposed procedures with a diverging dimensionality. Our results indicate that two commonly used hyper-priors on g (the Zellner-Siow prior and the beta-prime prior) yield inconsistent Bayes factors due to the presence of an inconsistency region around the null model. We propose a new class of hyper-priors to avoid this inconsistency problem. Simulation studies on two-way ANOVA models are conducted to compare the performance of the proposed priors with that of some existing ones in the literature.
Bio: Min Wang obtained his Ph.D. from Clemson University in May 2013, where his research mainly focused on Bayesian hypothesis testing and variable selection in high dimensional regression analysis. After his graduation, Dr. Wang joined the faculty of Michigan Tech University in August 2013 and received early promotion and tenure to Associate Professor in 2017. In January 2018, He started his new job as an Associate Professor at Texas Tech University. His teaching interests include Bayesian Statistics, Engineering Statistics, Statistical Programming, and Linear Models. His current research lies broadly in the areas of Bayesian statistics, multivariate analysis, statistical modelling, and quality and reliability engineering, all in the pragmatic and theoretical aspects.
Contact Name: Li Li
Contact Email: email@example.com