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The algebra of reversible Markov chains

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  • Giovanni Pistone
  • Maria Rogantin

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. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Giovanni Pistone & Maria Rogantin, 2013. "The algebra of reversible Markov chains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 269-293, April.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:2:p:269-293
    DOI: 10.1007/s10463-012-0368-7
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    Cited by:

    1. Abraham Martín del Campo & Sarah Cepeda & Caroline Uhler, 2017. "Exact Goodness-of-Fit Testing for the Ising Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 285-306, June.

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