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    Local composite likelihood for spatial point processes

    Access Status
    Fulltext not available
    Authors
    Baddeley, Adrian
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Baddeley, A. 2016. Local composite likelihood for spatial point processes. Spatial Statistics.
    Source Title
    Spatial Statistics
    DOI
    10.1016/j.spasta.2017.03.001
    ISSN
    2211-6753
    School
    Department of Mathematics and Statistics
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP130104470
    URI
    http://hdl.handle.net/20.500.11937/52852
    Collection
    • Curtin Research Publications
    Abstract

    © 2017 Elsevier B.V.We develop a general approach to spatial inhomogeneity in the analysis of spatial point pattern data. The ideas of local likelihood (or 'geographically weighted regression') are applied to the composite likelihoods that are commonly used for spatial point processes. For Poisson point processes, local likelihood is already known; for Gibbs point processes we develop a local version of Besag's pseudolikelihood; for Cox point processes and Neyman-Scott cluster processes we develop a local version of the Palm likelihood of Ogata and Katsura. Using recent results for composite likelihood and for spatial point processes, we develop tools for statistical inference, including intensity approximations, variance estimators, localised tests for the significance of a covariate effect, and global tests of homogeneity. Computationally efficient approximations are available using the Fast Fourier Transform. We develop methods for bandwidth selection, which may also be useful for smoothing dependent spatial data. There are mathematical connections to existing exploratory methods such as the scan statistic, local indicators of spatial association, and point process residuals. The methods are demonstrated on three example datasets, and R code is supplied.

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      In the statistical analysis of spatial point patterns, it is often important to investigate whether the point pattern depends on spatial covariates. This paper describes nonparametric (kernel and local likelihood) methods ...
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