Pseudo-likelihood equations for Potts model on higher-order neighborhood systems: A quantitative approach for parameter estimation in image analysis
Alexandre L. M. Levada, Nelson D. A. Mascarenhas, and Alberto Tannús
Source: Braz. J. Probab. Stat. Volume 23, Number 2 (2009), 120-140.
Abstract
This paper presents analytical pseudo-likelihood (PL) equations for Potts Markov random field (MRF) model parameter estimation on higher-order neighborhood systems by expanding the derivative of the log-PL function based on the enumeration of all possible contextual configuration patterns given a neighborhood system. The proposed equations allow the modeling of less restrictive neighborhood systems in a large number of MRF applications in a computationally feasible way. To evaluate the proposed estimation method we propose a hypothesis testing approach, derived by approximating the asymptotic variance of MPL parameter estimators using the observed Fisher information. The definition of the asymptotic variance, together with the test size α and p-values, provide a complete framework for quantitative analysis. Experiments with synthetic images generated by Markov chain Monte Carlo simulation methods assess the accuracy of the proposed estimation method, indicating that higher-order neighborhood systems reduce the MPL estimator asymptotic variance and improve estimation performance.
Keywords: Markov random fields; Potts model; maximum pseudo-likelihood estimation; Markov chain Monte Carlo simulation
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Permanent link to this document: http://projecteuclid.org/euclid.bjps/1256562754
Digital Object Identifier: doi:10.1214/08-BJPS018
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