Quantile approximations for risk evaluation in spatial Cox processes
Log-Gaussian Cox processes define a flexible class of spatial models that allow the description of a wide variety of dependence effects in point patterns through random heterogeneities in the underlying intensity function. In this work, a quantile-based framework for risk evaluation is developed, focusing on both the intensity and the associated event counts over a spatial region. Theoretical expressions for intensity quantiles are derived, while the quantiles of the counts, arising from a Poisson-lognormal distribution, are approximated using moment-based normal approximations. The empirical performance of these approximations is assessed through simulation, analyzing their accuracy in terms of bias and variability under alternative settings, with stochastic components driven by different covariance structures. Finally, this methodology is applied to a real dataset of forest fires, illustrating its usefulness for spatial risk assessment.
Keywords: Log-Gaussian Cox process quantile approximation risk maps spatial point process Value-at-Risk