CONSISTENCY OF MARKOV CHAIN QUASI-MONTE CARLO ON CONTINUOUS STATE SPACES

• 成果类型: Article
• 署名作者: Chen, S.; Dick, J.; Owen, A. B.
• 署名单位: Stanford University; University of New South Wales Sydney
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS831
• 发表日期: 2011
• 页码: 673-701
• 关键词: simulation; SEQUENCES

摘要

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than lid. U(0, 1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.