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Perfect posterior simulation for mixture and hidden Markov models

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Berthelsen, Kasper K., Breyer, Laird A. and Roberts, Gareth O.. (2010) Perfect posterior simulation for mixture and hidden Markov models. LMS Journal of Computation and Mathematics, Vol.13 . pp. 246-259. ISSN 1461-1570

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Official URL: http://dx.doi.org/10.1112/S1461157007000022

Abstract

In this paper we present an application of the read-once coupling from the past algorithm to problems in Bayesian inference for latent statistical models. We describe a method for perfect simulation from the posterior distribution of the unknown mixture weights in a mixture model. Our method is extended to a more general mixture problem, where unknown parameters exist for the mixture components, and to a hidden Markov model.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Mathematical models, Mathematical statistics, Distribution (Probability theory)

Journal or Publication Title:

LMS Journal of Computation and Mathematics

Publisher:

Cambridge University Press

ISSN:

1461-1570

Official Date:

10 August 2010

Dates:

Date	Event
10 August 2010	Published

Volume:

Vol.13

Number of Pages:

Page Range:

pp. 246-259

Identification Number:

10.1112/S1461157007000022

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

European Union (EU), Engineering and Physical Sciences Research Council (EPSRC), Statens naturvidenskabelige forskningsråd (Denmark) [Natural Science Research Council]

Grant number:

ERB-FMRX-CT96-0095 (EU), 272-06-0442 (DNSRC)

References:

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hidden Markov models', Technical Report 07-23, Centre for Research in Statistical Methodology (CRiSM),
University of Warwick, 2007.
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Methodol. Comput. Appl. Probab. 31 (2005) 407{437.
3. L. A. Breyer and G. O. Roberts, `Catalytic perfect simulation', Methodol. Comput. Appl. Probab. 3
(2001) 161{177.
4. G. Casella, K. L. Mengersen, C. P. Robert and D. M. Titterington, `Perfect samplers for mixtures
of distributions', J. Roy. Statist. Soc. Ser. B 64 (2002) 777{790.
5. J. Diebolt and C. P. Robert, `Estimation of finite mixture distributions through Bayesian sampling',
J. Roy. Statist. Soc. Ser. B 56 (1994) 363{375.
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distributions', Stat. Comput. 9 (1999) 223{252.
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mechanics', Random Structures Algorithms 9 (1996) 223{252.
8. G. O. Roberts and J. S. Rosenthal, `One-shot coupling for certain stochastic recursive sequences',
Stochastic Process. Appl. 99 (2002) 195{208.
9. D. B. Wilson, `How to couple from the past using a read-once source of randomness', Random Structures
Algorithms 16 (2000) 85{113.