Decision-theoretic properties of possibilistic inferential models

Ryan Martin
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:183-195, 2025.

Abstract

Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability properties in that context. The present paper develops an IM framework for decision making, and investigates the decision-theoretic implications of the IM’s reliability guarantees. I show that the IM’s assessment of an action’s quality, defined by a Choquet integral, will not be too optimistic compared to that of an oracle. This ensures that the IM tends not to favor actions that the oracle doesn’t also favor, hence a IM is reliable for decision making too. In a certain special class of structured statistical models, further connections can be made between the IM’s recommended actions and those recommended by Bayesian/fiducial frameworks, from which certain optimality conclusions can be drawn.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-martin25a, title = {Decision-theoretic properties of possibilistic inferential models}, author = {Martin, Ryan}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {183--195}, 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/martin25a/martin25a.pdf}, url = {https://proceedings.mlr.press/v290/martin25a.html}, abstract = {Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability properties in that context. The present paper develops an IM framework for decision making, and investigates the decision-theoretic implications of the IM’s reliability guarantees. I show that the IM’s assessment of an action’s quality, defined by a Choquet integral, will not be too optimistic compared to that of an oracle. This ensures that the IM tends not to favor actions that the oracle doesn’t also favor, hence a IM is reliable for decision making too. In a certain special class of structured statistical models, further connections can be made between the IM’s recommended actions and those recommended by Bayesian/fiducial frameworks, from which certain optimality conclusions can be drawn.} }
Endnote
%0 Conference Paper %T Decision-theoretic properties of possibilistic inferential models %A Ryan Martin %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-martin25a %I PMLR %P 183--195 %U https://proceedings.mlr.press/v290/martin25a.html %V 290 %X Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability properties in that context. The present paper develops an IM framework for decision making, and investigates the decision-theoretic implications of the IM’s reliability guarantees. I show that the IM’s assessment of an action’s quality, defined by a Choquet integral, will not be too optimistic compared to that of an oracle. This ensures that the IM tends not to favor actions that the oracle doesn’t also favor, hence a IM is reliable for decision making too. In a certain special class of structured statistical models, further connections can be made between the IM’s recommended actions and those recommended by Bayesian/fiducial frameworks, from which certain optimality conclusions can be drawn.
APA
Martin, R.. (2025). Decision-theoretic properties of possibilistic inferential models. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:183-195 Available from https://proceedings.mlr.press/v290/martin25a.html.

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