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

页码：269 / 293

页数：25

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