ON THE OPTIMAL TRANSITION MATRIX FOR MARKOV CHAIN MONTE CARLO SAMPLING

被引：15

作者：

Chen, Ting-Li ^{[1
]}

Chen, Wei-Kuo ^{[2
]}

Hwang, Chii-Ruey ^{[2
]}

Pai, Hui-Ming ^{[3
]}

机构：

[1] Acad Sinica, Inst Stat Sci, Taipei 11529, Taiwan

[2] Acad Sinica, Inst Math, Taipei 11529, Taiwan

[3] Natl Taipei Univ, Dept Stat, Taipei 23741, Taiwan

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2012年 / 50卷 / 05期

关键词：

Markov chain; Markov chain Monte Carlo; asymptotic variance; average-case analysis; worst-case analysis; rate of convergence; reversibility; nonreversibility;

D O I：

10.1137/110832288

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Let chi be a finite space and let pi be an underlying probability on chi. For any real-valued function f defined on chi, we are interested in calculating the expectation of f under pi. Let X-0, X-1,..., X-n,... be a Markov chain generated by some transition matrix P with invariant distribution pi. The time average, 1/n Sigma(n-1)(k=0) f(X-k), is a reasonable approximation to the expectation, E-pi[f(X)]. Which matrix P minimizes the asymptotic variance of 1/n Sigma(n-1)(k=0) f(X-k)? The answer depends on f. Rather than a worst-case analysis, we will identify the set of P's that minimize the average asymptotic variance, averaged with respect to a uniform distribution on f.

引用

页码：2743 / 2762

页数：20

共 13 条

[1]

[Anonymous], 1980, Finite Markov Processes and their Applications

[2]

[Anonymous], 1999, REVERSIBLE MARKOV CH

[3]

Diaconis P, 2009, B AM MATH SOC, V46, P179

[4]

FRIGESSI A, 1993, J R STAT SOC B, V55, P205