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Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

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  • Ninna Vihrs
  • Jesper Møller
  • Alan E. Gelfand

Abstract

In this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

Suggested Citation

  • Ninna Vihrs & Jesper Møller & Alan E. Gelfand, 2022. "Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 185-210, March.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:185-210
    DOI: 10.1111/sjos.12509
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    References listed on IDEAS

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