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Perfect posterior simulation for mixture and hidden Markov models

Part of: Markov processes Parametric inference

Published online by Cambridge University Press:  01 August 2010

Kasper K. Berthelsen ,
Laird A. Breyer  and
Gareth O. Roberts
Kasper K. Berthelsen
Affiliation:
Department of Mathematical Sciences, Aalborg University, 9220 Aalborg Øst, Denmark (email: [email protected])
Laird A. Breyer
Affiliation:
Department of Statistics, Lancaster University, Bailrigg Lancaster LA1 4YF, United Kingdomhttp://www.lbreyer.com/
Gareth O. Roberts
Affiliation:
Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom (email: [email protected])

Abstract

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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.

MSC classification

Secondary: 60J22: Computational methods in Markov chains 62F12: Asymptotic properties of estimators
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 246 - 259
Copyright
Copyright © London Mathematical Society 2010

References

[1] Berthelsen, K. K., Breyer, L. A. and Roberts, G. O., ‘Perfect posterior simulation for mixture and hidden Markov models’, Technical Report 07-23, Centre for Research in Statistical Methodology (CRiSM), University of Warwick, 2007.Google Scholar
[2] Beskos, A. and Roberts, G. O., ‘One-shot CFTP; application to a class of truncated Gaussian densities’, Methodol. Comput. Appl. Probab. 31 (2005) 407–437.CrossRefGoogle Scholar
[3] Breyer, L. A. and Roberts, G. O., ‘Catalytic perfect simulation’, Methodol. Comput. Appl. Probab. 3 (2001) 161–177.CrossRefGoogle Scholar
[4] Casella, G., Mengersen, K. L., Robert, C. P. and Titterington, D. M., ‘Perfect samplers for mixtures of distributions’, J. Roy. Statist. Soc. Ser. B 64 (2002) 777–790.CrossRefGoogle Scholar
[5] Diebolt, J. and Robert, C. P., ‘Estimation of finite mixture distributions through Bayesian sampling’, J. Roy. Statist. Soc. Ser. B 56 (1994) 363–375.Google Scholar
[6] Hobert, J. P., Robert, C. P. and Titterington, D. M., ‘On perfect simulation for some mixtures of distributions’, Stat. Comput. 9 (1999) 223–252.Google Scholar
[7] Propp, J. G. and Wilson, D. B., ‘Exact sampling with coupled Markov chains and applications to statistical mechanics’, Random Structures Algorithms 9 (1996) 223–252.3.0.CO;2-O>CrossRefGoogle Scholar
[8] Roberts, G. O. and Rosenthal, J. S., ‘One-shot coupling for certain stochastic recursive sequences’, Stochastic Process. Appl. 99 (2002) 195–208.CrossRefGoogle Scholar
[9] Wilson, D. B., ‘How to couple from the past using a read-once source of randomness’, Random Structures Algorithms 16 (2000) 85–113.Google Scholar