Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods

被引：0
作者：
Andreas Eberle
Carlo Marinelli
机构：
[1] Universität Bonn,Institut für Angewandte Mathematik
[2] Università di Bolzano,Facoltà di Economia
来源：
Probability Theory and Related Fields | 2013年 / 155卷
关键词：
Markov chain Monte Carlo; Sequential Monte Carlo; Importance sampling; Spectral gap; Dirichlet forms; Functional inequalities; Feynman–Kac formula; 65C05; 60J25; 60B10; 47H20; 47D08;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.
引用
收藏
页码：665 / 701
页数：36
相关论文
共 42 条
[1]  
Cappé O.(2004)Population Monte Carlo J. Comput. Graph. Stat. 13 907-929
[2]  
Guillin A.(2011)A nonasymptotic theorem for unnormalized Feynman–Kac particle models Ann. Inst. H. Poincaré Probab. Stat. 47 629-649
[3]  
Marin J.M.(2002)A sequential particle filter method for static models Biometrika 89 539-551
[4]  
Robert C.P.(2004)Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference Ann. Stat. 32 2385-2411
[5]  
Cérou F.(2006)Sequential Monte Carlo samplers J. R. Stat. Soc. B 68 411-436
[6]  
Del Moral P.(2001)On the stability of interacting processes with applications to filtering and genetic algorithms Ann. Inst. H. Poincaré Probab. Stat. 37 155-194
[7]  
Guyader A.(1999)On the convergence and applications of generalized simulated annealing SIAM J. Control Optim. 37 1222-1250
[8]  
Chopin N.(1996)The cutoff phenomenon in finite Markov chains Proc. Nat. Acad. Sci. USA 93 1659-1664
[9]  
Chopin N.(2010)Total variation cutoff in birth-and-death chains Probab. Theory Relat. Fields 146 61-85
[10]  
Del Moral P.(2007)Minimum variance importance sampling via population Monte Carlo ESAIM Probab. Stat. 11 427-447
12345