Statistics – Methodology
Scientific paper
2010-04-20
Journal of the American Statistical Association, volume 105, 2010, pp. 170--180
Statistics
Methodology
31 pages, 4 figures. Different pagination from journal version due to incompatible style files but same content; the supplemen
Scientific paper
10.1198/jasa.2009.tm08326
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 {\em Laplace-Gaussian filter} (LGF) 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 LGF can deliver superior results in a small fraction of the computing time.
Kass Robert E.
Koyama Shinsuke
Pérez-Bolde Lucia Castellanos
Shalizi Cosma Rohilla
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