2019/07/06 by Karl Oskar Ekvall, Galin L. Jones, Ekvall, Karl Oskar +1
Mathematics · Computer Science · #Markov Chains and Monte Carlo Methods #Bayesian Methods and Mixture Models #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1907.03170
We study the convergence properties of a collapsed Gibbs sampler for Bayesian\nvector autoregressions with predictors, or exogenous variables. The Markov\nchain generated by our algorithm is shown to be geometrically ergodic\nregardless of whether the number of observations in the underlying vector\nautoregression is small or large in comparison to the order and dimension of\nit. In a convergence complexity analysis, we also give conditions for when the\ngeometric ergodicity is asymptotically stable as the number of observations\ntends to infinity. Specifically, the geometric convergence rate is shown to be\nbounded away from unity asymptotically, either almost surely or with\nprobability tending to one, depending on what is assumed about the data\ngenerating process. This result is one of the first of its kind for practically\nrelevant Markov chain Monte Carlo algorithms. Our convergence results hold\nunder close to arbitrary model misspecification.\n