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The algebra of reversible Markov chains

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Abstract

For a Markov chain, both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical models. One of the results of this study is an algebraic parameterization of reversible Markov transitions and their invariant probability.

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Authors and Affiliations

  1. Collegio Carlo Alberto, Via Real Collegio 30, 10024, Moncalieri, Italy

    Giovanni Pistone

  2. DIMA Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy

    Maria Piera Rogantin

Authors
  1. Giovanni Pistone
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  2. Maria Piera Rogantin
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Corresponding author

Correspondence to Giovanni Pistone.

Additional information

G. Pistone was supported by de Castro Statistics Initiative, Collegio Carlo Alberto, Moncalieri, Italy.

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Pistone, G., Rogantin, M.P. The algebra of reversible Markov chains. Ann Inst Stat Math 65, 269–293 (2013). https://doi.org/10.1007/s10463-012-0368-7

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  • DOI: https://doi.org/10.1007/s10463-012-0368-7

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