IP Scoring Rules: Foundations and Applications
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:256-264, 2019.
The mathematical foundations of imprecise probability theory (IP) have been in place for 25 years, and IP has proved successful in practice. But IP methods lack rigorous accuracy-centered, philosophical justifications. Traditional Bayesian methods can be justified using epistemic scoring rules, which measure the accuracy of the estimates that they produce. But there has been little work extending these justifications to the IP framework. This paper makes plea for the IP community to embrace this research programme. The plea comes in three parts. Firstly, I outline some initial work developing scoring rules for imprecise probabilities — IP scoring rules — and using them to shore up the philosophical foundations of IP. Secondly, I explain why a range of impossibility results for IP scoring rules should not dissuade the IP community from working on the foundations of IP scoring rules. Finally, I highlight one potential applications for IP scoring rules: IP aggregation.