Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo 论文
1995Journal of the American Statistical Association引用 475
Markov Chains and Monte Carlo MethodsStatistical Methods and Bayesian InferenceBayesian Methods and Mixture Models
摘要
this paper, we provide a method (Theorem 5) for proving rigorous, a priori bounds on the number of iterations required until satisfactory convergence has taken place. We feel that such bounds provide increased confidence in the results of MCMC, and allow for improved analysis of the efficiency of various algorithms. It is our hope that the methods presented here can be applied quite generally, to many different Markov chain samplers. Our method involves establishing minorization conditions (splits) for Markov chains (see section 2) to establish results about convergence of MCMC. This amounts to showing that the Markov chain satisfies a condition of the form P