# Score-based calibration testing for multivariate forecast distributions

arXiv: https://arxiv.org/abs/2211.16362 · HTML: https://mlsanity.com/paper/2211.16362/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2022.

## 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)
- [From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks](https://mlsanity.com/paper/2311.16333/) (2023)
- [Enhancing multivariate post-processed visibility predictions utilizing CAMS forecasts](https://mlsanity.com/paper/2406.14159/) (2024)
- [Calibrated Multivariate Distributional Regression with Pre-Rank Regularization](https://mlsanity.com/paper/2601.22895/) (2026)
- [Hierarchies of Calibration: Classification meets Regression](https://mlsanity.com/paper/2606.03245/) (2026)
- [Calibrated Multivariate Regression with Localized PIT Mappings](https://mlsanity.com/paper/2409.10855/) (2024)

## Abstract (arXiv)

Calibration tests based on the probability integral transform (PIT) are routinely used to assess the quality of univariate distributional forecasts. However, PIT-based calibration tests for multivariate distributional forecasts face various challenges. We propose two new types of tests based on proper scoring rules, which overcome these challenges. They arise from a general framework for calibration testing in the multivariate case, introduced in this work. The new tests have good size and power properties in simulations and solve various problems of existing tests. We apply the tests to forecast distributions for macroeconomic and financial time series data.