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August, 1995 Hidden Markov Random Fields
Hans Kunsch, Stuart Geman, Athanasios Kehagias
Ann. Appl. Probab. 5(3): 577-602 (August, 1995). DOI: 10.1214/aoap/1177004696


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.


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Hans Kunsch. Stuart Geman. Athanasios Kehagias. "Hidden Markov Random Fields." Ann. Appl. Probab. 5 (3) 577 - 602, August, 1995.


Published: August, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0842.60046
MathSciNet: MR1359820
Digital Object Identifier: 10.1214/aoap/1177004696

Primary: 60G60
Secondary: 62M05

Keywords: Hidden Markov models , Markov random fields , speech models , textures

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 3 • August, 1995
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