ON THE ERGODICITY OF THE ADAPTIVE METROPOLIS ALGORITHM ON UNBOUNDED DOMAINS

• 成果类型: Article
• 署名作者: Saksman, Eero; Vihola, Matti
• 署名单位: University of Helsinki; University of Jyvaskyla
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP682
• 发表日期: 2010
• 页码: 2178-2203
• 关键词: monte-carlo algorithms; CONVERGENCE; mcmc

摘要

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptation sets, independent estimates of the growth rate of the AM chain and the corresponding geometric drift constants. The ergodicity result of the constrained process is obtained through a modification of the approach due to Andrieu and Moulines [Ann. Appl. Probab. 16 (2006) 1462-1505].