WHICH ERGODIC AVERAGES HAVE FINITE ASYMPTOTIC VARIANCE?

• 成果类型: Article
• 署名作者: Deligiannidis, George; Lee, Anthony
• 署名单位: University of Oxford; University of Warwick; University of Bristol; Alan Turing Institute
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1358
• 发表日期: 2018
• 页码: 2309-2334
• 关键词: approximate bayesian computation; deterministic markov-processes; metropolis algorithms; geometric ergodicity; limit-theorem; chains; CONVERGENCE; hastings; distributions; Kernels

摘要

We show that the class of L-2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L-2 functions for which ergodic averages of its associated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple sufficient condition for all ergodic averages of L-2 functions of the primary variable in a pseudo-marginal Markov chain to have finite asymptotic variance.