scoringrules.crps_quantile

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scoringrules.crps_quantile#

scoringrules.crps_quantile(obs: ArrayLike, fct: Array, alpha: Array, m_axis: int = -1, *, backend: Backend = None) → Array#

Approximate the CRPS from quantile predictions via the Pinball Loss.

It is based on the notation in [1].

The CRPS can be approximated as the mean pinball loss for all quantile forecasts \(F_q\) with level \(q \in Q\):

\[\text{quantileCRPS} = \frac{2}{|Q|} \sum_{q \in Q} PB_q\]

where the pinball loss is defined as:

\[\begin{split}\text{PB}_q = \begin{cases} q(y - F_q) &\text{if} & y \geq F_q \\ (1-q)(F_q - y) &\text{else.} & \\ \end{cases}\end{split}\]
Parameters:
obsarray_like

The observed values.

fctarray_like

The predicted forecast ensemble, where the ensemble dimension is by default represented by the last axis.

alphaarray_like

The percentile levels. We expect the quantile array to match the axis (see below) of the forecast array.

m_axisint

The axis corresponding to the ensemble. Default is the last axis.

backendstr, optional

The name of the backend used for computations. Defaults to numba if available, else numpy.

Returns:
qcrpsarray_like

An array of CRPS scores for each forecast, which should be averaged to get meaningful values.

References

[1]

Berrisch, J., & Ziel, F. (2023). CRPS learning. Journal of Econometrics, 237(2), 105221. Available at https://arxiv.org/abs/2102.00968.

# TODO: add example

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