Implement Variogram Score

[jc-macdonald]

Summary

The variogram score is a multivariate proper scoring rule that is less sensitive to ensemble size than the energy score.

Function

Function	Description
variogram_score(obs, fct; p=0.5)	Variogram score of order p

Algorithm

$$ \text{VS}_p(F, \mathbf{y}) = \sum_{i,j} w_{ij} \left( |y_i - y_j|^p - \mathbb{E}|X_i - X_j|^p \right)^2 $$

References

• Scheuerer, M., & Hamill, T. M. (2015). Variogram-based proper scoring rules for probabilistic forecasts of multivariate quantities. Monthly Weather Review.

Acceptance Criteria

• Matches scoringrules Python on reference data
• Supports custom weight matrix
• Default p=0.5 with option for other orders