Speaker: Vivek Roy, Associate Professor, Department of Statistics, Iowa State University

Title: Convergence rate results for some manifold MCMC algorithms

Abstract: Diffusions based and Hamiltonian dynamics-based methods, such as the Metropolis adjusted Langevin algorithms (MALA), and the Hamiltonian
Monte Carlo (HMC) have emerged as powerful Metropolis-Hastings algorithms. After discussing different manifold variants of MALA and HMC, we describe convergence results for some of these manifold Markov chains. These theoretical results have important practical implications as these justify the use of asymptotically valid Monte Carlo standard errors for Markov chain-based estimates. We verify the general results on convergence properties of the manifold MCMC algorithms in the context of conditional simulation from the two most popular generalized linear mixed models (GLMMs), namely the binomial GLMM with the logit link and the Poisson GLMM with the log link. Finally, we investigate the mixtures of the manifold HMC transition kernels with the manifold MALA kernels by studying their convergence properties and applying the algorithms to several benchmark examples.
 

(This talk is based on joint works with Lijin Zhang, James Brofos, and Roy Lederman.)