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Article overview
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Convergence Analysis of a Collapsed Gibbs Sampler for Bayesian Vector Autoregressions | | Karl Oskar Ekvall
; Galin L. Jones
; | | Date: |
6 Jul 2019 | | Abstract: | We propose a collapsed Gibbs sampler for Bayesian vector autoregressions with
predictors, or exogenous variables, and study the proposed algorithm’s
convergence properties. The Markov chain generated by our algorithm converges
to its stationary distribution at least as fast as those of competing
(non-collapsed) Gibbs samplers and 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. 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. Our results are
among the first of their kind for practically relevant Markov chain Monte Carlo
algorithms. | | Source: | arXiv, 1907.3170 | | Services: | Forum | Review | PDF | Favorites | |
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