Implement Energy Score (multivariate)

[jc-macdonald]

Summary

The energy score is the multivariate generalization of CRPS.

Function

Function	Description
energy_score(obs::AbstractVector, fct::AbstractMatrix)	Energy score from ensemble forecast samples

Algorithm

$$ \text{ES}(F, \mathbf{y}) = \mathbb{E}|\mathbf{X} - \mathbf{y}| - \frac{1}{2}\mathbb{E}|\mathbf{X} - \mathbf{X}'| $$

where norms are Euclidean. The sample estimate uses all pairwise distances in the ensemble.

References

• Gneiting, T., & Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation.

Acceptance Criteria

• Matches scoringrules (Python) on reference data
• Reduces to CRPS for univariate case
• Handles varying ensemble sizes