Evaluation of space-time point process models using super-thinning

Rescaling, thinning, and superposition are useful methods for the residual analysis of spatial-temporal point processes. These techniques involve transforming the original point process into a new process that is a homogeneous Poisson process if and only if the fitted model is correct, so that one may inspect the residual process using standard tests for homogeneity as a means of assessing the goodness-of-fit of the model. Unfortunately, when the modeled conditional intensity of the original process is volatile, tests of homogeneity performed on residuals on the basis of these three residual methods tend to have low power. For such circumstances, we propose the method of super-thinning, which combines thinned residuals and superposition. This technique involves the use of a tuning parameter, k, which controls how much thinning and superposition are performed to homogenize the process. The method is applied to the assessment of a parametric space–time point process model for the origin times and epicentral locations of recent major California earthquakes. Copyright © 2012 John Wiley & Sons, Ltd.