Evaluating epidemic forecasts in an interval format.

For practical reasons, many forecasts of case, hospitalization and death counts in the context of the current COVID-19 pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub run by the UMass-Amherst Influenza Forecasting Center of Excellence. Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This note provides an overview of how established methods for the evaluation of quantile and interval forecasts can be applied to epidemic forecasts. Specifically, we discuss the computation and interpretation of the weighted interval score, which is a proper score that approximates the continuous ranked probability score. It can be interpreted as a generalization of the absolute error to probabilistic forecasts and allows for a simple decomposition into a measure of sharpness and penalties for over- and underprediction.