IP Scoring Rules: Foundations and Applications

Jason Konek
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:256-264, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-konek19a, title = {IP Scoring Rules: Foundations and Applications}, author = {Konek, Jason}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {256--264}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/konek19a/konek19a.pdf}, url = {https://proceedings.mlr.press/v103/konek19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T IP Scoring Rules: Foundations and Applications %A Jason Konek %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-konek19a %I PMLR %P 256--264 %U https://proceedings.mlr.press/v103/konek19a.html %V 103 %X 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.
APA
Konek, J.. (2019). IP Scoring Rules: Foundations and Applications. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:256-264 Available from https://proceedings.mlr.press/v103/konek19a.html.

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