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Consistency of Maximum Likelihood and Pseudo-Likelihood Estimators for Gibbs Distributions

  • B. Gidas
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 10)

Abstract

We prove that the Maximum Likelihood and Pseudo-likelihood estimators for the parameters of Gibbs distributions (equivalently Markov Random Fields) over ℤd, d≥l, are consistent even at points of “first” or “higher-order” phase transitions. The distributions are parametrized by points in a finite-dimensional Euclidean space ℝm, m≥l, and the single spin state space is either a finite set or a compact metric space. Also, the underlying interactions need not be of finite range.

Keywords

Asymptotic Normality Perceptual Inference Single Photon Emission Tomography Strict Convexity Gibbs Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • B. Gidas
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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