Smoothing With Couplings of Conditional Particle Filters

• 成果类型: Article
• 署名作者: Jacob, Pierre E.; Lindsten, Fredrik; Schon, Thomas B.
• 署名单位: Harvard University; Linkoping University; Uppsala University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1548856
• 发表日期: 2020
• 页码: 721-729
• 关键词: sequential monte-carlo; parameter-estimation; Uniform Ergodicity; state; gibbs; simulation; STABILITY

摘要

In state-space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and CI can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly informative observations, and for a realistic Lotka-Volterra model with an intractable transition density. Supplementary materials for this article are available online.