Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.

Mathematics and Statistics

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Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC. / Fearnhead, Paul.
In: Statistics and Computing, Vol. 18, No. 2, 06.2008, p. 151-171.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fearnhead, P 2008, 'Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.', Statistics and Computing, vol. 18, no. 2, pp. 151-171. https://doi.org/10.1007/s11222-007-9045-8

APA

Fearnhead, P. (2008). Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC. Statistics and Computing, 18(2), 151-171. https://doi.org/10.1007/s11222-007-9045-8

Vancouver

Fearnhead P. Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC. Statistics and Computing. 2008 Jun;18(2):151-171. doi: 10.1007/s11222-007-9045-8

Author

Fearnhead, Paul. / Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC. In: Statistics and Computing. 2008 ; Vol. 18, No. 2. pp. 151-171.

Bibtex

@article{f505b6f93eb84f2abe39afeb22135329,

title = "Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.",

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",

author = "Paul Fearnhead",

year = "2008",

month = jun,

doi = "10.1007/s11222-007-9045-8",

language = "English",

volume = "18",

pages = "151--171",

journal = "Statistics and Computing",

issn = "0960-3174",

publisher = "Springer Netherlands",

number = "2",

}

RIS

TY - JOUR

T1 - Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.

AU - Fearnhead, Paul

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

KW - Diffusions

KW - Forward-Backward Algorithm

KW - Importance Sampling

KW - Missing Data

KW - Particle Filter

KW - Population Genetics

U2 - 10.1007/s11222-007-9045-8

DO - 10.1007/s11222-007-9045-8

M3 - Journal article

VL - 18

SP - 151

EP - 171

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -

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