Gibbs-Markov random fields on networks

Part of the Springer Series in Statistics book series (SSS)


Without additional hypotheses, conditional distributions {v i} are not generally compatible in this way. In this chapter, we will begin by describing a general family of conditional distributions called Gibbs specifications that are compatible without further conditions; Gibbs specifications are characterized by potentials. Their importance is enhanced by the Hammersley-Clifford theorem showing that Markov random fields are Gibbs random fields with local potentials. Besag’s auto-models are a particularly simple subclass of Markov random fields that are useful in spatial statistics.


Joint Distribution Conditional Distribution Ising Model Gibbs Sampling Gibbs Measure 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di StatisticaUniversità Ca’ Foscari VeneziaVenezialtaly
  2. 2.SAMOS Université Paris IParisFrance

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