Calibration diagnostics for point process models via the probability integral transform

TL;DR

This paper introduces PIT-based diagnostics for validating point process models, enabling assessment of calibration and detection of inconsistencies in intensity and interaction structure across various dimensions.

Contribution

It develops a simple, explicit PIT diagnostic method for point process model validation, applicable to models of any dimension and capable of detecting calibration issues.

Findings

PIT diagnostics effectively assess model calibration.

The method detects inconsistencies in intensity and interaction.

Explicit calculations are provided for Poisson models.

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.