MARKOV-CHAINS FOR EXPLORING POSTERIOR DISTRIBUTIONS

• 成果类型: Article
• 署名作者: TIERNEY, L
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325750
• 发表日期: 1994
• 页码: 1701-1728
• 关键词: steady-state simulation; models

摘要

Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several Variance reduction techniques and also gives guidance on the choice of sample size and allocation.