Computational methods for complex stochastic systems: a review of some alternatives to MCMC |
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Authors: | Paul Fearnhead |
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Institution: | (1) Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK |
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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. |
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Keywords: | Diffusions Forward-backward algorithm Importance sampling Missing data Particle filter Population genetics |
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