Local scale invariance and robustness of proper scoring rules

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• David Bolin (King Abdullah University of Science and Technology (KAUST))
• Friday 06 June 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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RCLW02 - Calibrating prediction uncertainty : statistics and machine learning perspectives

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most popular proper scoring rules, such as the continuous ranked probability score (CRPS), give more importance to observations with large uncertainty, which can lead to unintuitive rankings. To describe this issue, we define the concept of local scale invariance for scoring rules. A new class of generalized proper kernel scoring rules is derived and as a member of this class we propose the scaled CRPS (SCRPS). This new proper scoring rule is locally scale invariant and, therefore, works in the case of varying uncertainty. Like the CRPS , it is computationally available for output from ensemble forecasts, and does not require the ability to evaluate densities of forecasts. We also extend the concept of local scale invariance to proper scoring rules for extremes and introduce a weighted version of the SCRPS . Finally, we discuss robustness properties of proper scoring rules and introduce robust version of both the CRPS and the SCRPS .  

This talk is part of the Isaac Newton Institute Seminar Series series.

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