Scaling limits for the transient phase of local Metropolis-Hastings algorithms
成果类型：
Article
署名作者：
Christensen, OF; Roberts, GO; Rosenthal, JS
署名单位：
Lancaster University; Aarhus University; University of Toronto
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/j.1467-9868.2005.00500.x
发表日期：
2005
页码：
253-268
关键词：
摘要：
The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular-to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.