Approximate Methods for State-Space Models

• 成果类型: Article
• 署名作者: Koyama, Shinsuke; Perez-Bolde, Lucia Castellanos; Shalizi, Cosma Rohilla; Kass, Robert E.
• 署名单位: Carnegie Mellon University; Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; The Santa Fe Institute
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08326
• 发表日期: 2010
• 页码: 170-180
• 关键词: position; ensemble; arm

摘要

State-space models provide an important body of techniques for analyzing time series. but their use requires estimating Unobserved states The optimal estimate of the state Is its conditional expectation given the observation histories. and computing this expectation is hard when there are nonlinearities Existing filtering methods, including sequential Monte Carlo. tend to be either inaccurate or slow In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models. which uses Laplace's method. an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution This Laplace Gaussian fillet (LGE) gives fast. recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data We find that the LGE can deliver superior results in a small fraction of the computing time This article has supplementary material online