B0182
Title: Lower bounds on the rate of convergence for Metropolis-Hastings algorithms
Authors: Galin Jones - University of Minnesota (United States) [presenting]
Abstract: Practitioners are often left tuning Metropolis-Hastings algorithms by trial and error or using optimal scaling guidelines to avoid poor empirical performance. We develop general lower bounds on the convergence rates of Metropolis-Hastings algorithms to study their computational complexity, paying particular attention to geometrically ergodic Markov chains. General lower bounds on the mixing times are also developed when the algorithms are not necessarily geometrically ergodic, and similar lower bounds are given in Wasserstein distances. We consider the implications in real data applications using Metropolis-Hastings for Bayesian logistic regression with either flat priors or Zellener's G-prior for the regression coefficients.
