Abstract:Safety-critical prediction systems, such as autonomous vehicles, weather forecasters, and medical monitors, commonly rely on probabilistic forecasters. These forecasters make predictions about possible future outcomes, and their quality and robustness needs to be validated and certified. Often, only accuracy -- the mean of the predictions -- is evaluated against true outcomes. However, for safety-critical scenarios and decision making under uncertainty, the full distributional properties of the forecasts should be checked: do the observed prediction errors actually follow the forecasted probability distributions? To this end, we introduce a framework for calibration checks: statistical tests that validate distributional properties of forecasts when measured over many samples. In order to support ease-of-use in real-world operations, these checks produce a single accept/reject decision for data collected from a forecaster. This contrasts typical calibration calculations which produce one or multiple continuous calibration scores and require expertise to implement in a validation workflow. We further support operationalization by introducing modifications to calibration testing that (a) reject only overconfident predictions, allowing for pessimistic or cautious predictions in safety-critical settings, and (b) tolerate small, operationally acceptable deviations even for large numbers of validation samples. We organize the calibration checking process into a modular pipeline comprising four steps: (i) the data model, (ii) the chosen metric, (iii) the hypothesis formulation, and (iv) the testing procedure. Each step consists of independently swappable components, thereby supporting a large variety of possible use-cases and trade-offs. We demonstrate the applicability of the framework on two complementary example problems, weather forecasting and robot pose estimation.
| Comments: | 36 pages, 22 figures. Manuscript prepared with Typst |
| Subjects: | Methodology (stat.ME); Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.26479 [stat.ME] |
| (or arXiv:2604.26479v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2604.26479 arXiv-issued DOI via DataCite (pending registration) |
From: Romeo Valentin [view email]
[v1]
Wed, 29 Apr 2026 09:43:55 UTC (1,342 KB)
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