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Title of Journal: Ann Inst Stat Math

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Abbravation: Annals of the Institute of Statistical Mathematics

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Springer-Verlag

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10.1016/0001-6160(74)90095-9

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1572-9052

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Smoothing algorithms for state–space models

Authors: Mark Briers Arnaud Doucet Simon Maskell
Publish Date: 2009/06/09
Volume: 62, Issue: 1, Pages: 61-
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Abstract

Twofilter smoothing is a principled approach for performing optimal smoothing in nonlinear nonGaussian state–space models where the smoothing distributions are computed through the combination of ‘forward’ and ‘backward’ time filters The ‘forward’ filter is the standard Bayesian filter but the ‘backward’ filter generally referred to as the backward information filter is not a probability measure on the space of the hidden Markov process In cases where the backward information filter can be computed in closed form this technical point is not important However for general state–space models where there is no closed form expression this prohibits the use of flexible numerical techniques such as Sequential Monte Carlo SMC to approximate the twofilter smoothing formula We propose here a generalised twofilter smoothing formula which only requires approximating probability distributions and applies to any state–space model removing the need to make restrictive assumptions used in previous approaches to this problem SMC algorithms are developed to implement this generalised recursion and we illustrate their performance on various problems

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  2. Maximum likelihood estimation in the proportional hazards cure model
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  4. Two-step estimation procedures for inhomogeneous shot-noise Cox processes
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  16. On sum of 0–1 random variables I. Univariate case
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