ECUAS_n: A family of metrics for principled evaluation of uncertainty-augmented systems

Uncertainty estimates in machine learning are typically evaluated using generic metrics such as the negative log-likelihood and expected calibration error, yet good performance on such metrics does not necessarily imply high utility in downstream decisions. We introduce decision-alignment, a criterion that reveals which evaluation metrics meaningfully align with downstream utilities. Applying this framework, we show that many widely used uncertainty metrics are either misaligned with common decision problems or encode pathological prior beliefs about the downstream task. We then propose prior-weighted utility metrics, a special class of proper scoring rules that provides decision-aligned uncertainty evaluation. Across benchmark experiments and real-world case studies, our metrics consistently align with realized decision utility, while conventional metrics do not. Our results surface flaws in the current UQ evaluation protocol and offer a principled extension of existing metrics toward decision-relevant UQ evaluation.

Language-model agents increasingly emit uncertainty signals throughout a trajectory, but existing agentic UQ evaluations often conflate ranking usefulness with probabilistic truthfulness. AUROC, AUPRC, risk-coverage, Trajectory ECE, and scalarized trajectory scores evaluate discrimination, binwise calibration, or collapsed summaries, but do not strictly elicit the full prefix-conditioned success-probability trace $q_t = P^π(Y=1 | H_t)$. Building on prequential proper scoring, we introduce the Trajectory Proper Score (TPS), a predictor-agnostic family of strictly proper trajectory-level scoring rules for any per-step uncertainty signal calibrated into a probability of eventual success. We prove that TPS strictly elicits the success-probability process under complete observation, within the chosen score family and weight schedule. We extend the construction to administratively censored trajectories by projecting the complete-data score onto the observable stopped prefix, yielding an exact $q_Z$-weighted reduced score and a tractable approximation when $q_Z$ is unestimated. We further show that common trajectory evaluators target weaker objects than the full prefix-conditioned probability process: Trajectory ECE is resolution-blind, while scalarized Trajectory Brier elicits only the collapsed scalar, not the full trace. Experiments on StrategyQA, Tau2-Bench, HotpotQA, and WebShop show that these theoretical distinctions are operationally visible: probability recalibration can substantially change TPS while leaving rank metrics nearly unchanged, and the tractable censored approximation can change the verdict relative to complete-only evaluation.

Uncertainty quantification (UQ) is essential for reliable decision-making in safety-critical applications in probabilistic machine learning. For regression problems, dominant scalar UQ approaches - notably, those based on proper scoring rules - measure uncertainty via pointwise predictive risk. This can lead to counterintuitive results when the target statistic is not the conditional expectation. We propose an alternative framework, in which uncertainty is characterised by the volume of the most probable subset of a distribution's support. QUEST (Quantifying Uncertainty via highest dEnSiTy regions) is a novel approach to UQ based on the concentration of Lebesgue measure at a distribution's peak(s), evaluated at one or more values of a robustness parameter $α$. We establish connections between our measures and classical statistics from information theory and economics. We show that, unlike popular alternatives based on proper scoring rules, QUEST measures of epistemic and aleatoric uncertainty satisfy a set of axioms adapted from the UQ literature, including monotonicity under distributional spread and invariance to location shifts. Selective prediction benchmarks confirm that QUEST performs favourably against standard measures such as variance and differential entropy.