Evaluation of stochastic trajectory-based epidemic models using the energy score

Scoring rules are critical for evaluating the predictive performance of epidemic models by quantifying how well their projections and forecasts align with observed data. In this study, we introduce the energy score as a performance metric for stochastic trajectory-based epidemic models. As a multivariate extension of the continuous ranked probability score (CRPS), the energy score provides a single, unified measure for time-series predictions. It evaluates both calibration and sharpness by considering the distances between individual trajectories and observed data, as well as the inter-trajectory variability. We provide an overview of how the energy score can be applied to assess both scenario projections and forecasts in this format, with a particular focus on a detailed analysis of the Scenario Modeling Hub results for the 2023-2024 influenza season. By comparing the energy score to the widely used weighted interval score (WIS), we demonstrate its utility as a tool for evaluating epidemic models, especially in scenarios requiring integration of predictions across multiple target outcomes into a single, interpretable metric.