Comparative evaluation of point process forecasts

Abstract

Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules, which are statistically principled tools for the comparative evaluation of predictive performance, to the point process setting, and place both new and existing methodology in this framework. With reference to earthquake likelihood model testing, we demonstrate that extant techniques apply in much broader contexts than previously thought. In particular, the Poisson log-likelihood can be used for theoretically principled comparative forecast evaluation in terms of cell expectations. We illustrate the approach in a simulation study and in a comparative evaluation of operational earthquake forecasts for Italy.

arXiv comment40 pages, 14 figures

References in corpus (7)

• Determinantal point process models and statistical inference : Extended version
• Power-law models for infectious disease spread
• Theory and Applications of Proper Scoring Rules
• Assessment of Point Process Models for Earthquake Forecasting
• Residual analysis methods for space--time point processes with applications to earthquake forecast models in California
• Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts
• Comparative evaluation of point process forecasts

Cited by in corpus (2)

• Enhancing the statistical evaluation of earthquake forecasts -- An application to Italy
• Comparative evaluation of point process forecasts