On determining the order of Markov dependence of an observed process governed by a hidden Markov model

  • Authors:

  • R. J. Boys;D. A. Henderson

  • Affiliations:

  • Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK. Tel.: +44 (0)191 222 7297/ E-mail: Richard.Boys@ncl.ac.uk;Department of Statistics, The Open University, Milton Keynes, MK7 6AA, UK. Tel.: +44 (0)1908 652 030/ E-mail: d.a.henderson@open.ac.uk (Corresponding author)

  • Venue:
  • Scientific Programming - Hidden Markov Models
  • Year:
  • 2002

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Abstract

This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior) distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.