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    Consistent estimation of the basic neighborhood of Markov random fields

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    TalataZ_AS_34(1)123.pdf (238.0Kb)
    Issue Date
    2006-10-05
    Author
    Csiszar, Imre
    Talata, Zsolt
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    For Markov random fields on ℤd with finite state space, we address the statistical estimation of the basic neighborhood, the smallest region that determines the conditional distribution at a site on the condition that the values at all other sites are given. A modification of the Bayesian Information Criterion, replacing likelihood by pseudo-likelihood, is proved to provide strongly consistent estimation from observing a realization of the field on increasing finite regions: the estimated basic neighborhood equals the true one eventually almost surely, not assuming any prior bound on the size of the latter. Stationarity of the Markov field is not required, and phase transition does not affect the results.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1214/009053605000000912.
    URI
    http://hdl.handle.net/1808/17226
    DOI
    https://doi.org/10.1214/009053605000000912
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Csiszár, Imre; Talata, Zsolt. Consistent estimation of the basic neighborhood of Markov random fields. Ann. Statist. 34 (2006), no. 1, 123--145. http://dx.doi.org/10.1214/009053605000000912.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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