Resolution of probabilistic weather forecasts with application in disease management

Predictive systems in disease management often incorporate weather data among the disease risk factors, and sometimes this comes in the form of forecast weather data rather than observed weather data. In such cases, it is useful to have an evaluation of the operational weather forecast, in addition to the evaluation of the disease forecasts provided by the predictive system. Typically, weather forecasts and disease forecasts are evaluated using different methodologies. However, the information theoretic quantity expected mutual information provides a basis for evaluating both kinds of forecast. Expected mutual information is an appropriate metric for the average performance of a predictive system over a set of forecasts. Both relative entropy (a divergence, measuring information gain) and specific information (an entropy difference, measuring change in uncertainty) provide a basis for the assessment of individual forecasts.