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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
Volume:	Vol.13
Number of Pages:	14
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:	1. K. K. Berthelsen, L. A. Breyer and G. O. Roberts, `Perfect posterior simulation for mixture and hidden Markov models', Technical Report 07-23, Centre for Research in Statistical Methodology (CRiSM), University of Warwick, 2007. 2. A. Beskos and G. O. Roberts, `One-shot CFTP; application to a class of truncated Gaussian densities', 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. 6. J. P. Hobert, C. P. Robert and D. M. Titterington, `On perfect simulation for some mixtures of distributions', Stat. Comput. 9 (1999) 223{252. 7. J. G. Propp and D. B.Wilson, `Exact sampling with coupled Markov chains and applications to statistical 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.
URI:	http://wrap.warwick.ac.uk/id/eprint/4841