The Iterated Auxiliary Particle Filter

• 成果类型: Article
• 署名作者: Guarniero, Pieralberto; Johansen, Adam M.; Lee, Anthony
• 署名单位: University of Warwick
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1222291
• 发表日期: 2017
• 页码: 1636-1647
• 关键词: CENTRAL-LIMIT-THEOREM; MONTE-CARLO METHODS; strategies; likelihood; simulation; inference

摘要

We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given amodel and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of twisted models: each member is specified by a sequence of positive functions. and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi*-auxiliary particle filter's estimate of L has zero variance. In practical applications, psi* is unknown so the psi*- auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate psi* and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm.