Proper scoring rule balancing sharpness (narrower intervals score
better) against calibration (penalising intervals that miss the
observed value). Lower is better.
Usage
edaphos_interval_score(observed, lower, upper, alpha = 0.05)
Arguments
- observed, lower, upper
Numeric vectors.
- alpha
Nominal miscoverage level (1 - nominal PICP). Default
0.05 for a 95% prediction interval.
Value
Non-negative numeric scalar (mean over the test set).
Details
$$IS_\alpha = (u - \ell) + \frac{2}{\alpha}(\ell - y) \mathbb 1\{y < \ell\}
+ \frac{2}{\alpha}(y - u) \mathbb 1\{y > u\}.$$
References
Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring
rules, prediction, and estimation. Journal of the American
Statistical Association 102(477), 359-378.
