文章基本信息

标题：Convergence analysis of a collapsed Gibbs sampler for Bayesian vector autoregressions
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作者：Karl Oskar Ekvall ; Galin L. Jones
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：1
页码：691-721
DOI：10.1214/21-EJS1800
语种：English
出版社：Institute of Mathematical Statistics
摘要：We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algorithm is shown to be geometrically ergodic regardless of whether the number of observations in the underlying vector autoregression is small or large in comparison to the order and dimension of it. In a convergence complexity analysis, we also give conditions for when the geometric ergodicity is asymptotically stable as the number of observations tends to infinity. Specifically, the geometric convergence rate is shown to be bounded away from unity asymptotically, either almost surely or with probability tending to one, depending on what is assumed about the data generating process. This result is one of the first of its kind for practically relevant Markov chain Monte Carlo algorithms. Our convergence results hold under close to arbitrary model misspecification.
关键词：Convergence complexity analysis;geometric ergodicity;Markov chain Monte Carlo;Bayesian vector autoregression;Gibbs sampler