A spatio-temporal multi-scale model for Geyer saturation point process: application to forest fire occurrences
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Since most natural phenomena exhibit dependence at multiple scales (e.g. earthquake and forest fire occurrences), single-scale spatio-temporal Gibbs models are unrealistic in many applications. This motivates statisticians to construct the multi-scale generalizations of the classical Gibbs models and to develop new Gibbs point process models. In this paper, we extend the spatial multi-scale Geyer point process model to the spatio-temporal framework. The model is implemented using the birth-death Metropolis-Hastings algorithm in R. In a simulation study, we compare the common methods for statistical inference in Gibbs models, as the pseudo-likelihood and logistic likelihood approaches. Finally, we fit this new model to a forest fire dataset in France.
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