Open Access
Translator Disclaimer
2021 Convergence analysis of a collapsed Gibbs sampler for Bayesian vector autoregressions
Karl Oskar Ekvall, Galin L. Jones
Electron. J. Statist. 15(1): 691-721 (2021). DOI: 10.1214/21-EJS1800

Abstract

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.

Citation

Download Citation

Karl Oskar Ekvall. Galin L. Jones. "Convergence analysis of a collapsed Gibbs sampler for Bayesian vector autoregressions." Electron. J. Statist. 15 (1) 691 - 721, 2021. https://doi.org/10.1214/21-EJS1800

Information

Received: 1 February 2020; Published: 2021
First available in Project Euclid: 21 January 2021

Digital Object Identifier: 10.1214/21-EJS1800

Subjects:
Primary: 62F15 , 62M05 , 62M10

Keywords: Bayesian vector autoregression , Convergence complexity analysis , geometric ergodicity , Gibbs sampler , Markov chain Monte Carlo

JOURNAL ARTICLE
31 PAGES


SHARE
Vol.15 • No. 1 • 2021
Back to Top