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November, 1995 A Generalized Maximum Pseudo-Likelihood Estimator for Noisy Markov Fields
David J. Barsky, Alberto Gandolfi
Ann. Appl. Probab. 5(4): 1095-1125 (November, 1995). DOI: 10.1214/aoap/1177004608

Abstract

In this paper we present an asymptotic estimator, obtained by observing a noisy image, for the parameters of both a stationary Markov random field and an independent Bernoulli noise. We first estimate the parameter of the noise by solving a polynomial equation of moderate degree (about 6-7 in the one-dimensional Ising model and about 10-15 in the two-dimensional Ising model, for instance) and then apply the maximum pseudo-likelihood method after removing the noise. Our method requires no extra simulation and is likely to be applicable to any Markov random field, in any dimension. Here we present the general theory and some examples in one dimension; more interesting examples in two dimensions will be discussed at length in a companion paper.

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David J. Barsky. Alberto Gandolfi. "A Generalized Maximum Pseudo-Likelihood Estimator for Noisy Markov Fields." Ann. Appl. Probab. 5 (4) 1095 - 1125, November, 1995. https://doi.org/10.1214/aoap/1177004608

Information

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

zbMATH: 0849.62055
MathSciNet: MR1384368
Digital Object Identifier: 10.1214/aoap/1177004608

Subjects:
Primary: 62M40
Secondary: 62F12

Keywords: consistent estimator , Markov random fields , Maximum pseudo-likelihood estimator

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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