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Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation
Author(s) -
Vihrs Ninna,
Møller Jesper,
Gelfand Alan E.
Publication year - 2022
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12509
Subject(s) - approximate bayesian computation , point process , bayesian inference , mathematics , inference , cox process , bayesian probability , gaussian process , statistical inference , computation , algorithm , point (geometry) , statistical model , gaussian , statistical physics , computer science , artificial intelligence , statistics , poisson process , physics , geometry , quantum mechanics , poisson distribution
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.