Comparative evaluation of point process forecasts

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