Optimal scaling for partially updating MCMC algorithms

• 成果类型: Article
• 署名作者: Neal, Peter; Roberts, Gareth
• 署名单位: University of Manchester; Lancaster University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000791
• 发表日期: 2006
• 页码: 475-515
• 关键词: metropolis; DIFFUSIONS

摘要

[it this paper we shall consider optimal scaling problems for high-dimensional Metropolis-Hastings algorithms where updates call be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, Which tunes the overall algorithm acceptance rate to be 0.234. holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore. the optimal efficiency obtainable is independent of the dimensionality of the update rule. This has important implications for the MCMC practitioner since high-dimensional updates are generally computationally more demanding. so that lower-dimensional updates are therefore to be preferred. Similar results with rather different conclusions are given for so-called Langevin updates. In this case. it is found that high-dimensional updates are frequently most efficient. even taking into account computing costs.