The Annals of Applied Probability

Hidden Markov Random Fields

Hans Kunsch, Stuart Geman, and Athanasios Kehagias

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A noninvertible function of a first-order Markov process or of a nearest-neighbor Markov random field is called a hidden Markov model. Hidden Markov models are generally not Markovian. In fact, they may have complex and long range interactions, which is largely the reason for their utility. Applications include signal and image processing, speech recognition and biological modeling. We show that hidden Markov models are dense among essentially all finite-state discrete-time stationary processes and finite-state lattice-based stationary random fields. This leads to a nearly universal parameterization of stationary processes and stationary random fields, and to a consistent nonparametric estimator. We show the results of attempts to fit simple speech and texture patterns.

Article information

Ann. Appl. Probab., Volume 5, Number 3 (1995), 577-602.

First available in Project Euclid: 19 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60G60: Random fields
Secondary: 62M05: Markov processes: estimation

Hidden Markov models Markov random fields speech models textures


Kunsch, Hans; Geman, Stuart; Kehagias, Athanasios. Hidden Markov Random Fields. Ann. Appl. Probab. 5 (1995), no. 3, 577--602. doi:10.1214/aoap/1177004696.

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