Predictive Model Assessment for Count Data

Abstract

We discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data.
Our proposals include a nonrandomized version of the probability integral transform, marginal calibration diagrams, and
proper scoring rules, such as the predictive deviance. In case studies, we critique count regression models for patent data, and
assess the predictive performance of Bayesian age-period-cohort models for larynx cancer counts in Germany. The toolbox
applies in Bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes.