Title: Convergence analysis of a collapsed Gibbs sampler for Bayesian vector autoregressions
Authors: Karl Oskar Ekvall - Vienna University of Technology (Austria) [presenting]
Galin Jones - University of Minnesota (United States)
Abstract: The use of Markov chain Monte Carlo (MCMC) to explore posterior distributions is widespread in Bayesian statistics. In order to assess or ensure the reliability of an analysis using MCMC it is essential to understand some convergence properties of the chain in use. We discuss a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The emphasis is on how the algorithm's convergence rate is affected as the length of the sample path from the underlying vector autoregression increases. The main result, which is among the first of its kind for practically relevant MCMC algorithms, establishes an asymptotic upper bound on the convergence rate.