Elicitation for sets of probabilities and distributions

Mark J. Schervish, Teddy Seidenfeld, Ruobin Gong, Joseph B. Kadane, Rafael B. Stern
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:242-251, 2025.

Abstract

We investigate techniques for applying strictly proper scoring rules to elicit arbitrary sets of probabilities for an event and for eliciting sets of countably additive (finite dimensional) joint distributions. We contrast E-admissibility, Maximality, and $\Gamma$-Maximin as three IP decision rules for these elicitations. The techniques we investigate apply with sets of probabilities that need not be convex or even connected, and with distributions that may lack moments. We address some challenges to applying these techniques for eliciting merely finitely additive probability distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-schervish25a, title = {Elicitation for sets of probabilities and distributions}, author = {Schervish, Mark J. and Seidenfeld, Teddy and Gong, Ruobin and Kadane, Joseph B. and Stern, Rafael B.}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {242--251}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/schervish25a/schervish25a.pdf}, url = {https://proceedings.mlr.press/v290/schervish25a.html}, abstract = {We investigate techniques for applying strictly proper scoring rules to elicit arbitrary sets of probabilities for an event and for eliciting sets of countably additive (finite dimensional) joint distributions. We contrast E-admissibility, Maximality, and $\Gamma$-Maximin as three IP decision rules for these elicitations. The techniques we investigate apply with sets of probabilities that need not be convex or even connected, and with distributions that may lack moments. We address some challenges to applying these techniques for eliciting merely finitely additive probability distributions.} }
Endnote
%0 Conference Paper %T Elicitation for sets of probabilities and distributions %A Mark J. Schervish %A Teddy Seidenfeld %A Ruobin Gong %A Joseph B. Kadane %A Rafael B. Stern %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-schervish25a %I PMLR %P 242--251 %U https://proceedings.mlr.press/v290/schervish25a.html %V 290 %X We investigate techniques for applying strictly proper scoring rules to elicit arbitrary sets of probabilities for an event and for eliciting sets of countably additive (finite dimensional) joint distributions. We contrast E-admissibility, Maximality, and $\Gamma$-Maximin as three IP decision rules for these elicitations. The techniques we investigate apply with sets of probabilities that need not be convex or even connected, and with distributions that may lack moments. We address some challenges to applying these techniques for eliciting merely finitely additive probability distributions.
APA
Schervish, M.J., Seidenfeld, T., Gong, R., Kadane, J.B. & Stern, R.B.. (2025). Elicitation for sets of probabilities and distributions. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:242-251 Available from https://proceedings.mlr.press/v290/schervish25a.html.

Related Material