Probabilistic Forecasting

A probabilistic forecast takes the form of a predictive probability distribution over future quantities or events of interest. Probabilistic forecasting aims to maximize the sharpness of the predictive distributions, subject to calibration, on the basis of the available information set. We formalize and study notions of calibration in a prediction space setting. In practice, probabilistic calibration can be checked by examining probability integral transform (PIT) histograms. Proper scoring rules such as the logarithmic score and the continuous ranked probability score serve to assess calibration and sharpness simultaneously. As a special case, consistent scoring functions provide decision-theoretically…