A1206
Title: Informed MCMC for Bayesian variable selection
Authors: Vivekananda Roy - Iowa State University (United States) [presenting]
Abstract: A Riemannian geometric framework for Markov chain Monte Carlo (MCMC) is developed where using the Fisher-Rao metric on the manifold of probability density functions (PDFs) informed proposal densities for Metropolis-Hastings (MH) algorithms are constructed. The square-root representation of PDFs is exploited, under which the Fisher-Rao metric boils down to the standard L2 metric, resulting in a straightforward implementation of the proposed geometric MCMC methodology. Unlike the random walk MH that blindly proposes a candidate state using no information about the target, the geometric MH algorithms effectively move an uninformed base density (e.g., a random walk proposal density) towards different global/local approximations of the target density. This general geometric framework is used to construct fast mixing and scalable MCMC algorithms for performing Bayesian variable selection based on a hierarchical Gaussian linear model with popular spike and slab priors. The superiority of the geometric MH algorithm over other MCMC schemes is demonstrated using extensive ultra-high dimensional simulation examples, as well as a real dataset from a genome-wide association study (GWAS) with close to a million markers.
