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

By Ninna Vihrs, Jesper Møller and Alan E. Gelfand
CSGB Research Reports
No. 05, April 2020

In this paper, 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 of this model is not expressible in closed form, but it is easy to simulate under the model. We therefore explain how to use approximate Bayesian computation (ABC) for statistical inference both for this specific model but also for spatial point process models in general. We suggest a method for model validation and comparison based on posterior predictions and global envelopes. We illustrate the ABC procedure and model comparison approach using both simulated point patterns and a real data example.

Keywords: Approximate Bayesian computation (ABC); doubly stochastic process; log Gaussian Cox process; model comparison; posterior prediction; Strauss process

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