One of the major purposes of statistical analysis is to make forecasts for the future, and to provide suitable measures of the uncertainty associated with them. Consequently, forecasts should be probabilistic in nature, taking the form of probability distributions over future quantities or events. With the advent of probabilistic forecasting in applications including weather and climate prediction, computational finance and macroeconomic forecasting, the need for principled statistical techniques for the comparison and evaluation of distributional forecasters is becoming critical. The project addresses this challenge by developing tools for the assessment of calibration and sharpness, including ramifications of the probability integral transform and the verification rank histogram, and furthering theoretical insight into the construction and characterization, the properties, and the computation of proper scoring rules with desirable properties, such as kernel scores, local scores and skill scores.
A major human desire is to make forecasts for the future. Forecasts characterize and reduce, but generally do not eliminate uncertainty. Consequently, predictions should be probabilistic in nature, pointing decision makers to alternative scenarios and assigning probabilities to potential future events. With the advent of probabilistic predictions in applications that include severe weather warnings as well as economic and demographic projections, the need for principled tools for the comparison and evaluation of probabilistic forecast techniques is becoming critical. In essence, probabilistic predictions ought to be calibrated and sharp, in the sense that they are statistically compatible with the scenarios and events that realize, and reduce uncertainty to the extent possible. The project studies and develops tools for the assessment of calibration and sharpness, which are tailored to prompt and guide improvements in probabilistic prediction methodologies. In addition to biomedical, environmental, economic and financial applications, the project informs the reorientation of national weather and climate prediction efforts towards probabilistic forecasting that has recently been recommended by the National Academies.