LMS Journal of Computation and Mathematics

Research Article

Perfect posterior simulation for mixture and hidden Markov models

Kasper K. Berthelsena1, Laird A. Breyera2 and Gareth O. Robertsa3

a1 Department of Mathematical Sciences, Aalborg University, 9220 Aalborg Øst, Denmark (email: kkb@math.aau.dk)

a2 Department of Statistics, Lancaster University, Bailrigg Lancaster LA1 4YF, United Kingdomhttp://www.lbreyer.com/

a3 Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom (email: gareth.o.roberts@warwick.ac.uk)

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.

(Received January 09 2007)

(Revised April 03 2009)

(Online publication August 2010)

2000 Mathematics Subject Classification

  • 60J22 (primary);
  • 62F12 (secondary)

Footnotes

This research was supported by the European Union TMR network ERB-FMRX-CT96-0095 on ‘Spatial and Computational Statistics’, by an Engineering and Physical Sciences Research Council grant, and by the Danish Natural Science Research Council (grant no. 272-06-0442).