Information Geometry of Reversible Markov Chains

@article{Wolfer2021InformationGO,
  title={Information Geometry of Reversible Markov Chains},
  author={Geoffrey Wolfer and Shun Watanabe},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.05669}
}
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… 
Geometric Aspects of Data-Processing of Markov Chains
We consider data-processing of Markov chains through the lens of information geometry. We first develop a theory of congruent Markov morphisms in the context of Markov kernels that we show to

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