metrics.crps_empirical()

Compute the empirical Continuous Ranked Probability Score (CRPS).

Usage

Source

metrics.crps_empirical(
    pred,
    truth,
)

The CRPS generalises the mean absolute error to probabilistic forecasts and is computed elementwise as

.. math::

\mathrm{CRPS}(F, y) = \mathbb{E}|X - y| - \tfrac{1}{2}\,\mathbb{E}|X - X'|,

where :math:X, X' are independent draws from the forecast distribution :math:F. The expectations are estimated from the forecast sample axis using the sorted-sample :math:O(n \log n) identity.

Parameters

pred: Float[Array, " sample *batch"] | Float[np.ndarray, " sample *batch"]

Forecast samples with the sample axis first, shape (sample, *batch).

truth: Float[Array, " *batch"] | Float[np.ndarray, " *batch"]

Ground-truth values with shape (*batch) (broadcastable to pred).

Returns

Float[Array, "*batch"]

Elementwise CRPS, one value per batch location.

References

Tilmann Gneiting, Adrian E. Raftery (2007). “Strictly Proper Scoring Rules, Prediction, and Estimation”. Journal of the American Statistical Association.