Over-relaxation methods and coupled Markov chains for Monte Carlo simulation

作     者：Barone, P Sebastiani, G Stander, J 

作者机构：CNR Ist Applicaz Calcolo Rome Italy Univ Plymouth Dept Math & Stat Plymouth PL4 8AA Devon England 

出 版 物：《STATISTICS AND COMPUTING》 (统计学与计算)

年 卷 期：2002年第12卷第1期

页      面：17-26页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：EU TMR, (ERB-FMRX-CT96-0095) Royal Society 

主　　题：coupled algorithms Gibbs sampler spectral radius 

摘      要：This paper is concerned with improving the performance of certain Markov chain algorithms for Monte Carlo simulation. We propose a new algorithm for simulating from multivariate Gaussian densities. This algorithm combines ideas from coupled Markov chain methods and from an existing algorithm based only on over-relaxation. The rate of convergence of the proposed and existing algorithms can be measured in terms of the square of the spectral radius of certain matrices. We present examples in which the proposed algorithm converges faster than the existing algorithm and the Gibbs sampler. We also derive an expression for the asymptotic variance of any linear combination of the variables simulated by the proposed algorithm. We outline how the proposed algorithm can be extended to non-Gaussian densities.