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  • LMS Journal of Computation and Mathematics, Volume 13
  • August 2010, pp. 246-259

Perfect posterior simulation for mixture and hidden Markov models

  • Kasper K. Berthelsen (a1), Laird A. Breyer (a2) and Gareth O. Roberts (a3)
  • DOI: http://dx.doi.org/10.1112/S1461157007000022
  • Published online: 01 August 2010
Abstract
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[3]L. A. Breyer and G. O. Roberts , ‘Catalytic perfect simulation’, Methodol. Comput. Appl. Probab. 3 (2001) 161177.

[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) 777790.

[6]J. P. Hobert , C. P. Robert and D. M. Titterington , ‘On perfect simulation for some mixtures of distributions’, Stat. Comput. 9 (1999) 223252.

[7]J. G. Propp and D. B. Wilson , ‘Exact sampling with coupled Markov chains and applications to statistical mechanics’, Random Structures Algorithms 9 (1996) 223252.

[8]G. O. Roberts and J. S. Rosenthal , ‘One-shot coupling for certain stochastic recursive sequences’, Stochastic Process. Appl. 99 (2002) 195208.

[9]D. B. Wilson , ‘How to couple from the past using a read-once source of randomness’, Random Structures Algorithms 16 (2000) 85113.

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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