Structured spatio-temporal shot-noise Cox point process models, with a view to modelling forest fires

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 to the analysis of a relatively large dataset 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.