# Tail calibration of probabilistic forecasts

arXiv: https://arxiv.org/abs/2407.03167 · HTML: https://mlsanity.com/paper/2407.03167/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2024.

## Built on by (most cited first, 7 of 7)

- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [Enforcing tail calibration when training probabilistic forecast models](https://mlsanity.com/paper/2506.13687/) (2025)
- [Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training](https://mlsanity.com/paper/2605.13175/) (2026)
- [Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rules](https://mlsanity.com/paper/2407.15900/) (2024)
- [Hierarchies of Calibration: Classification meets Regression](https://mlsanity.com/paper/2606.03245/) (2026)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)

## Abstract (arXiv)

Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts, existing evaluation techniques are ill-suited to the evaluation of tail properties of such forecasts. However, these tail properties are often of particular interest to forecast users due to the severe impacts caused by extreme outcomes. In this work, we introduce a general notion of tail calibration for probabilistic forecasts, which allows forecasters to assess the reliability of their predictions for extreme outcomes. We study the relationships between tail calibration and standard notions of forecast calibration, and discuss connections to peaks-over-threshold models in extreme value theory. Diagnostic tools are introduced and applied in a case study on European precipitation forecasts