2021
DOI: 10.1007/s41884-021-00061-7
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Information Geometry of Reversible Markov Chains

Abstract: We analyze the information geometric structure of time reversibility for parametric families of irreducible transition kernels of Markov chains. We define and characterize reversible exponential families of Markov kernels, and show that irreducible and reversible Markov kernels form both a mixture family and, perhaps surprisingly, an exponential family in the set of all stochastic kernels. We propose a parametrization of the entire manifold of reversible kernels, and inspect reversible geodesics. We define inf… Show more

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Cited by 8 publications
(24 citation statements)
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“…(1) Generating reversiblizations via geometric projections. This approach continues the line of work initiated in Billera and Diaconis (2001); Diaconis and Miclo (2009); Wolfer and Watanabe (2021), in which reversiblizations are viewed as projections under information divergences such as f -divergences. The advantage of this approach is that we can recover all known reversiblizations in a unified framework.…”
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confidence: 56%
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“…(1) Generating reversiblizations via geometric projections. This approach continues the line of work initiated in Billera and Diaconis (2001); Diaconis and Miclo (2009); Wolfer and Watanabe (2021), in which reversiblizations are viewed as projections under information divergences such as f -divergences. The advantage of this approach is that we can recover all known reversiblizations in a unified framework.…”
mentioning
confidence: 56%
“…It is instructive to note that our notions of projection are with respect to a fixed target π, while in Wolfer and Watanabe (2021) projections are onto the entire reversible set. In the context of Markov chain Monte Carlo, we are often given a target π for instance a posterior distribution in a Bayesian model, and in this setting it is not at all restrictive to consider and investigate projections onto L(π).…”
Section: Preliminariesmentioning
confidence: 99%
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