The algebra of reversible Markov chains

被引：4
|
作者：
Pistone, Giovanni [1 ]
Rogantin, Maria Piera [2 ]
机构：
[1] Coll Carlo Alberto, I-10024 Moncalieri, Italy
[2] Univ Genoa, DIMA, I-16146 Genoa, Italy
来源：
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2013年 / 65卷 / 02期
关键词：
Reversible Markov chain; Algebraic statistics; Toric ideal;
D O I：
10.1007/s10463-012-0368-7
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：269 / 293
页数：25
相关论文
共 50 条
  • [1] The algebra of reversible Markov chains
    Giovanni Pistone
    Maria Piera Rogantin
    Annals of the Institute of Statistical Mathematics, 2013, 65 : 269 - 293
  • [2] Accelerating reversible Markov chains
    Chen, Ting-Li
    Hwang, Chii-Ruey
    STATISTICS & PROBABILITY LETTERS, 2013, 83 (09) : 1956 - 1962
  • [3] Estimation in Reversible Markov Chains
    Annis, David H.
    Kiessler, Peter C.
    Lund, Robert
    Steuber, Tara L.
    AMERICAN STATISTICIAN, 2010, 64 (02): : 116 - 120
  • [4] A monotonicity in reversible Markov chains
    Lund, Robert
    Zhao, Ying
    Kiessler, Peter C.
    JOURNAL OF APPLIED PROBABILITY, 2006, 43 (02) : 486 - 499
  • [5] Markov states and chains on the CAR algebra
    Accardi, Luigi
    Fidaleo, Francesco
    Mukhamedov, Farruh
    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2007, 10 (02) : 165 - 183
  • [6] Preserving the Markov Property of Reduced Reversible Markov Chains
    Weber, Marcus
    Kube, Susanna
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, 2008, 1048 : 593 - 596
  • [7] A combinatorial approach to nearly uncoupled Markov chains I: Reversible Markov chains
    Tifenbach, R.M. (ryan.tifenbach@mun.ca), 1600, Kent State University (40):
  • [8] A COMBINATORIAL APPROACH TO NEARLY UNCOUPLED MARKOV CHAINS I: REVERSIBLE MARKOV CHAINS
    Tifenbach, Ryan M.
    ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2013, 40 : 120 - 147
  • [9] Multiple Ergodicity For Reversible Markov Chains
    Yuan LIU
    ActaMathematicaeApplicataeSinica, 2018, 34 (04) : 863 - 868
  • [10] Bayesian analysis for reversible Markov chains
    Diaconis, Persi
    Rolles, Silke W. W.
    ANNALS OF STATISTICS, 2006, 34 (03): : 1270 - 1292
12345