scoringrules.gksuv_ensemble

scoringrules.gksuv_ensemble(obs: ArrayLike, fct: Array, m_axis: int = -1, *, ens_w: Array = None, estimator: str = 'nrg', backend: Backend = None) → Array

Compute the univariate Gaussian Kernel Score (GKS) for a finite ensemble.

The GKS is the kernel score associated with the Gaussian kernel

\[k(x_{1}, x_{2}) = \exp \left(- \frac{(x_{1} - x_{2})^{2}}{2} \right).\]

Given an ensemble forecast \(F_{ens}\) comprised of members \(x_{1}, \dots, x_{M}\), the GKS is

\[\text{GKS}(F_{ens}, y)= - \frac{1}{M} \sum_{m=1}^{M} k(x_{m}, y) + \frac{1}{2 M^{2}} \sum_{m=1}^{M} \sum_{j=1}^{M} k(x_{m}, x_{j}) + \frac{1}{2}k(y, y)\]

If the fair estimator is to be used, then \(M^{2}\) in the second component of the right-hand-side is replaced with \(M(M - 1)\).

Parameters:

obsarray_like

The observed values.

fctarray_like

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

m_axisint

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

ens_warray

Weights assigned to the ensemble members. Array with the same shape as fct. Default is equal weighting. Weights are normalised so that they sum to one across the ensemble members.

estimatorstr

Indicates the estimator to be used.

backendstr

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

Returns:

score:

The GKS between the forecast ensemble and obs.

Examples

>>> import scoringrules as sr
>>> sr.gks_ensemble(obs, pred)