Calibration diagnostics for point process models via the probability integral transform

Abstract

We propose the use of the probability integral transform (PIT) for model validation in point process models. The simple PIT diagnostics assess the calibration of the model and can detect inconsistencies in both the intensity and the interaction structure. For the Poisson model, the PIT diagnostics can be calculated explicitly. Generally, the calibration may be assessed empirically based on random draws from the model and the method applies to processes of any dimension.