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    Variational estimators for the parameters of Gibbs point process models

    Access Status
    Open access via publisher
    Authors
    Baddeley, Adrian
    Dereudre, D.
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Baddeley, A. and Dereudre, D. 2013. Variational estimators for the parameters of Gibbs point process models. Bernoulli. 19 (3): pp. 905-930.
    Source Title
    Bernoulli
    DOI
    10.3150/12-BEJ419
    ISSN
    1350-7265
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/27366
    Collection
    • Curtin Research Publications
    Abstract

    This paper proposes a new estimation technique for fitting parametric Gibbs point process models to a spatial point pattern dataset. The technique is a counterpart, for spatial point processes, of the variational estimators for Markov random fields developed by Almeida and Gidas. The estimator does not require the point process density to be hereditary, so it is applicable to models which do not have a conditional intensity, including models which exhibit geometric regularity or rigidity. The disadvantage is that the intensity parameter cannot be estimated: inference is effectively conditional on the observed number of points. The new procedure is faster and more stable than existing techniques, since it does not require simulation, numerical integration or optimization with respect to the parameters © 2013 ISI/BS.

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