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December 2007 Distributions associated with general runs and patterns in hidden Markov models
John A. D. Aston, Donald E. K. Martin
Ann. Appl. Stat. 1(2): 585-611 (December 2007). DOI: 10.1214/07-AOAS125

Abstract

This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later patterns), and thus, the theory includes as special cases results for a large class of problems that have wide application. The unobserved state sequence is assumed to be Markovian with a general order of dependence. An auxiliary Markov chain is associated with the state sequence and is used to simplify the computations. Two examples are given to illustrate the use of the methodology. Whereas the first application is more to illustrate the basic steps in applying the theory, the second is a more detailed application to DNA sequences, and shows that the methods can be adapted to include restrictions related to biological knowledge.

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John A. D. Aston. Donald E. K. Martin. "Distributions associated with general runs and patterns in hidden Markov models." Ann. Appl. Stat. 1 (2) 585 - 611, December 2007. https://doi.org/10.1214/07-AOAS125

Information

Published: December 2007
First available in Project Euclid: 30 November 2007

zbMATH: 1126.62008
MathSciNet: MR2415748
Digital Object Identifier: 10.1214/07-AOAS125

Keywords: Competing patterns , CpG islands , finite Markov chain imbedding , generalized later patterns , higher-order hidden Markov models , sooner/later waiting time distributions

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.1 • No. 2 • December 2007
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