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Statistics and Computing

, Volume 18, Issue 2, pp 151–171 | Cite as

Computational methods for complex stochastic systems: a review of some alternatives to MCMC

  • Paul FearnheadEmail author
Article

Abstract

We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain; inferring structure in population genetics; and segmenting genetic divergence data.

Keywords

Diffusions Forward-backward algorithm Importance sampling Missing data Particle filter Population genetics 

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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