What is the effective sample size of a spatial point process?

Ian W. Renner*, David I. Warton, Francis K.C. Hui

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    Point process models are a natural approach for modelling data that arise as point events. In the case of Poisson counts, these may be fitted easily as a weighted Poisson regression. Point processes lack the notion of sample size. This is problematic for model selection, because various classical criteria such as the Bayesian information criterion (BIC) are a function of the sample size, n, and are derived in an asymptotic framework where n tends to infinity. In this paper, we develop an asymptotic result for Poisson point process models in which the observed number of point events, m, plays the role that sample size does in the classical regression context. Following from this result, we derive a version of BIC for point process models, and when fitted via penalised likelihood, conditions for the LASSO penalty that ensure consistency in estimation and the oracle property. We discuss challenges extending these results to the wider class of Gibbs models, of which the Poisson point process model is a special case.

    Original languageEnglish
    Pages (from-to)144-158
    Number of pages15
    JournalAustralian and New Zealand Journal of Statistics
    Issue number1
    Publication statusPublished - Mar 2021


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