Verbalizing LLM’s Higher-order Uncertainty via Imprecise Probabilities

Anita Yang, Krikamol Muandet, Michele Caprio, Siu Lun Chau, Masaki Adachi
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:7761-7779, 2026.

Abstract

Despite the growing demand for eliciting uncertainty from large language models ({LLMs}), empirical evidence suggests that {LLM} behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in *imprecise probabilities*, a principled framework for representing and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from {LLMs}, improving credibility and supporting downstream decision-making.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-yang26c, title = {Verbalizing {LLM}’s Higher-order Uncertainty via Imprecise Probabilities}, author = {Yang, Anita and Muandet, Krikamol and Caprio, Michele and Chau, Siu Lun and Adachi, Masaki}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {7761--7779}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26c/yang26c.pdf}, url = {https://proceedings.mlr.press/v337/yang26c.html}, abstract = {Despite the growing demand for eliciting uncertainty from large language models ({LLMs}), empirical evidence suggests that {LLM} behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in *imprecise probabilities*, a principled framework for representing and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from {LLMs}, improving credibility and supporting downstream decision-making.} }
Endnote
%0 Conference Paper %T Verbalizing LLM’s Higher-order Uncertainty via Imprecise Probabilities %A Anita Yang %A Krikamol Muandet %A Michele Caprio %A Siu Lun Chau %A Masaki Adachi %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-yang26c %I PMLR %P 7761--7779 %U https://proceedings.mlr.press/v337/yang26c.html %V 337 %X Despite the growing demand for eliciting uncertainty from large language models ({LLMs}), empirical evidence suggests that {LLM} behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in *imprecise probabilities*, a principled framework for representing and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from {LLMs}, improving credibility and supporting downstream decision-making.
APA
Yang, A., Muandet, K., Caprio, M., Chau, S.L. & Adachi, M.. (2026). Verbalizing LLM’s Higher-order Uncertainty via Imprecise Probabilities. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:7761-7779 Available from https://proceedings.mlr.press/v337/yang26c.html.

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