Title: Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression
Authors: Qian Qin - University of Minnesota (United States) [presenting]
James Hobert - University of Florida (United States)
Abstract: The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales with sample size, $n$, and/or number of covariates, $p$. The convergence complexity of Albert and Chib's algorithm for Bayesian probit regression is studied. By constructing convergence bounds with respect to some Wasserstein distance, it is found that, under reasonable data structures, the algorithm converges rapidly even when $n$ and $p$ are large.