Parameter Estimation in Pair-hidden Markov Models

  1. ANA ARRIBAS-GIL1,
  2. ELISABETH GASSIAT1,
  3. CATHERINE MATIAS2

Article first published online: 8 MAY 2006

DOI: 10.1111/j.1467-9469.2006.00513.x

Issue

Scandinavian Journal of Statistics

Scandinavian Journal of Statistics

Volume 33, Issue 4, pages 651–671, December 2006

Additional Information

How to Cite

ARRIBAS-GIL, A., GASSIAT, E. and MATIAS, C. (2006), Parameter Estimation in Pair-hidden Markov Models. Scandinavian Journal of Statistics, 33: 651–671. doi: 10.1111/j.1467-9469.2006.00513.x

Author Information

  1. 1

    Équipe Probabilités, Statistique et Modélisation, Université Paris-Sud

  2. 2

    Laboratoire Statistique et Génome, CNRS

*Catherine Matias, Laboratoire Statistique et Génome, Tour Evry 2, 523 pl. des Terrasses de l'Agora, 91 000 Evry, France. E-mail: matias@genopole.cnrs.fr

Publication History

  1. Issue published online: 8 MAY 2006
  2. Article first published online: 8 MAY 2006
  3. Received October 2005, in final form February 2006

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Keywords:

  • pair-hidden Markov models;
  • score parameters estimation;
  • sequence alignment;
  • TKF evolution model

Abstract.  This paper deals with parameter estimation in pair-hidden Markov models. We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model is biologically motivated and therefore naturally leads to restrictions on the parameter space. Existence of two different information divergence rates is established and a divergence property is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.

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