Distributions associated with general runs and patterns in hidden Markov models

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dc.creatorAston, John A. D.
dc.creatorMartin, Donald E. K.
dc.date2007-06-27
dc.date2007-12-13
dc.date.accessioned2026-07-07T08:49:24Z
dc.date.available2026-07-07T08:49:24Z
dc.descriptionThis 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOAS125 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0706.3985
dc.identifierhttp://arxiv.org/abs/0706.3985
dc.identifierAnnals of Applied Statistics 2007, Vol. 1, No. 2, 585-611
dc.identifierdoi:10.1214/07-AOAS125
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144286
dc.subjectMethodology
dc.subjectApplications
dc.subjectComputation
dc.titleDistributions associated with general runs and patterns in hidden Markov models
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