SEQUENTIAL MONTE CARLO SMOOTHING FOR GENERAL STATE SPACE HIDDEN MARKOV MODELS

• 成果类型: Article
• 署名作者: Douc, Randal; Garivier, Aurelien; Moulines, Eric; Olsson, Jimmy
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Lund University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP735
• 发表日期: 2011
• 页码: 2109-2145
• 关键词: nonlinear filters; STABILITY; approximations; simulation

摘要

Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles.