Implement Weighted Interval Score (WIS)

[jc-macdonald]

Summary

The WIS scores quantile/interval forecasts and is widely used in epidemiological forecasting (e.g., COVID-19 Forecast Hub).

Functions

Function	Description
wis(obs, lower, upper, α)	Single-interval WIS at level α
wis(obs, quantile_levels, quantile_values)	Multi-quantile WIS

Algorithm

For a central $(1-\alpha)\times100%$ prediction interval $[l, u]$:

$$ \text{IS}_\alpha(l, u, y) = (u - l) + \frac{2}{\alpha}(l - y)\mathbb{1}{y < l} + \frac{2}{\alpha}(y - u)\mathbb{1}{y > u} $$

WIS averages over K intervals plus the median.

References

• Bracher, J., Ray, E. L., Gneiting, T., & Reich, N. G. (2021). Evaluating epidemic forecasts in an interval format. PLoS Computational Biology.

Acceptance Criteria

• Single-interval and multi-quantile variants
• Perfect forecast scores 0
• Known-value test against scoringrules Python output