Structured Spatio-Temporal Shot-Noise Cox Point Process Models, with a View to Modelling Forest Fires |
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Authors: | JESPER MØ LLER, CARLOS DÍ AZ-AVALOS |
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Affiliation: | Department of Mathematical Sciences, Aalborg University; Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México |
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Abstract: | Abstract. Spatio-temporal Cox point process models with a multiplicative structure for the driving random intensity, incorporating covariate information into temporal and spatial components, and with a residual term modelled by a shot-noise process, are considered. Such models are flexible and tractable for statistical analysis, using spatio-temporal versions of intensity and inhomogeneous K -functions, quick estimation procedures based on composite likelihoods and minimum contrast estimation, and easy simulation techniques. These advantages are demonstrated in connection with the analysis of a relatively large data set consisting of 2796 days and 5834 spatial locations of fires. The model is compared with a spatio-temporal log-Gaussian Cox point process model, and likelihood-based methods are discussed to some extent. |
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Keywords: | composite likelihood Cox process forest fires inhomogeneous K-function intensity log-Gaussian process minimum contrast estimation multiplicative model pair correlation function Poisson process shot-noise process simulation spatio-temporal point process |
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