Topic: Title: Scoring rules for prediction Authors:  Valentina Mameli - University of Udine (Italy) [presenting]
Federica Giummole - University Ca Foscari Venice (Italy)
Abstract: Most of the methods nowadays employed for comparing probability forecasts are based on proper scoring rules. To our knowledge, the use of scoring rules is exclusively restricted to assess the quality of a given probabilistic forecast for a future random variable. However, in the prediction framework the use of these objects can be extended to provide a whole predictive distribution for the unknown of interest. We discuss the asymptotic properties of predictive distributions obtained by minimizing the divergence associated to different scoring rules. Some examples dealing with the Tsallis score, which includes as special cases some of the most used scoring rules, are taken into consideration. For some Gaussian models, the predictive distribution obtained by minimizing the Tsallis divergence is asymptotically equivalent to the one obtained from the Kullback-Liebler divergence. We also consider the class of weighted scoring rules that evaluate probability forecasts on the basis of a non-uniform baseline distribution representing the available information at the time of prediction. The divergences associated to certain weighted scoring rules are shown to be asymptotically equivalent to $\alpha$-divergences, for which optimal predictive distributions exist.