Smoothing With Couplings of Conditional Particle Filters

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.

在状态-空间模型中，平滑化指的是在给定与过程相关的噪声测量值的基础上，对潜在随机过程进行估计的任务。本研究提出了一种平滑期望的无偏估计器。无偏性质在方法论上具有优势：可以并行生成独立的估计器，并且可以从中心极限定理构建置信区间，以量化近似误差。为了设计无偏估计器，我们结合了针对马尔可夫链的通用去偏技术，以及用于平滑的马尔可夫链蒙特卡洛算法。由此产生的程序具有广泛的应用性，并且在数值实验中，我们发现去除偏差带来的方差增加是可管理的。在温和的假设下，我们证实了所提出估计器的有效性。在玩具模型上提供了数值实验，包括高信息观测的设置，以及具有难以处理的转移密度的现实Lotka–Volterra模型。本文的补充材料可在网上获取。