On adaptive Markov chain Monte Carlo algorithms

被引:189
作者
Atchadé, YF
Rosenthal, JS
机构
[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6NS, Canada
[2] Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada
关键词
adaptive Markov chain Monte Carlo; metropolis algorithm; mixingales; parameter tuning; Robbins-Monro algorithm;
D O I
10.3150/bj/1130077595
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
We look at adaptive Markov chain Monte Carlo algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the history of the process. We show under certain conditions that the stochastic process generated is ergodic, with appropriate stationary distribution. We use this result to analyse an adaptive version of the random walk Metropolis algorithm where the scale parameter sigma is sequentially adapted using a Robbins-Monro type algorithm in order to find the optimal scale parameter sigma(opt). We close with a simulation example.
引用
收藏
页码:815 / 828
页数:14
相关论文
共 18 条
[11]  
KUSHNER K, 2003, STOCHASTIC APPROXIMA
[12]  
Liu J. S., 2001, Monte Carlo strategies in scientific computing
[13]   COMPUTABLE BOUNDS FOR GEOMETRIC CONVERGENCE RATES OF MARKOV CHAINS [J].
Meyn, Sean P. ;
Tweedie, R. L. .
ANNALS OF APPLIED PROBABILITY, 1994, 4 (04) :981-1011
[14]   A STOCHASTIC APPROXIMATION METHOD [J].
ROBBINS, H ;
MONRO, S .
ANNALS OF MATHEMATICAL STATISTICS, 1951, 22 (03) :400-407
[15]   WEAK CONVERGENCE AND OPTIMAL SCALING OF RANDOM WALK METROPOLIS ALGORITHMS [J].
Roberts, G. O. ;
Gelman, A. ;
Gilks, W. R. .
ANNALS OF APPLIED PROBABILITY, 1997, 7 (01) :110-120
[16]   Optimal scaling for various Metropolis-Hastings algorithms [J].
Roberts, GO ;
Rosenthal, JS .
STATISTICAL SCIENCE, 2001, 16 (04) :351-367
[17]  
ROSENTHAL JS, 2004, ADAPTIVE MCMV JAVA A
[18]  
Spiegelhalter D., 1995, MARKOV CHAIN MONTE C