# Assessing the calibration of high-dimensional ensemble forecasts using rank histograms

arXiv: https://arxiv.org/abs/1310.0236 · HTML: https://mlsanity.com/paper/1310.0236/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2013.

## Built on by (most cited first, 6 of 6)

- [A Composite-Loss Graph Neural Network for the Multivariate Post-Processing of Ensemble Weather Forecasts](https://mlsanity.com/paper/2509.02784/) (2025)
- [Enhancing multivariate post-processed visibility predictions utilizing CAMS forecasts](https://mlsanity.com/paper/2406.14159/) (2024)
- [Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rules](https://mlsanity.com/paper/2407.15900/) (2024)
- [Self-attentive Transformer for Fast and Accurate Postprocessing of Temperature and Wind Speed Forecasts](https://mlsanity.com/paper/2412.13957/) (2024)
- [Hierarchies of Calibration: Classification meets Regression](https://mlsanity.com/paper/2606.03245/) (2026)
- [Can Deep Generative Models Reproduce Non-Stationary Gaussian Random Fields?](https://mlsanity.com/paper/2607.25929/) (2026)

## Abstract (arXiv)

Any decision making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This paper proposes new methods for empirically assessing forecast calibration in a multivariate setting where the probabilistic forecast is given by an ensemble of equally probable forecast scenarios. Multivariate properties are mapped to a single dimension through a pre-rank function and the calibration is subsequently assessed visually through a histogram of the ranks of the observation's pre-ranks. Average ranking assigns a pre-rank based on the average univariate rank while band depth ranking employs the concept of functional band depth where the centrality of the observation within the forecast ensemble is assessed. Several simulation examples and a case study of temperature forecast trajectories at Berlin Tegel Airport in Germany demonstrate that both multivariate ranking methods can successfully detect various sources of miscalibration and scale efficiently to high dimensional settings.