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Scientific Programming
Volume 10 (2002), Issue 3, Pages 241-251
http://dx.doi.org/10.1155/2002/683164

On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model

R.J. Boys1 and D.A. Henderson2

1Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK
2Department of Statistics, The Open University, Milton Keynes, MK7 6AA, UK

Received 28 September 2002; Accepted 28 September 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.