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

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 realizati...

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Bibliographic Details
Published in:Scandinavian journal of statistics Vol. 49; no. 1; pp. 185 - 210
Main Authors: Vihrs, Ninna, Møller, Jesper, Gelfand, Alan E.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.03.2022
Subjects:
Agglomeration
approximate Bayesian computation
Bayesian analysis
doubly stochastic process
Gaussian process
log Gaussian Cox process
model comparison
posterior prediction
Statistical inference
Strauss process
ISSN:0303-6898, 1467-9469
Online Access:Get full text
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Summary: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.
Bibliography:Funding information
The Danish Council for Independent Research | Natural Sciences, 7014‐00074; Villum Fonden, 8721
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content type line 14
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12509