scoringrules.dssmv_ensemble

scoringrules.dssmv_ensemble(obs: Array, fct: Array, m_axis: int = -2, v_axis: int = -1, *, bias: bool = False, backend: Backend = None) → Array

Compute the Dawid-Sebastiani-Score for a finite multivariate ensemble.

The Dawid-Sebastiani Score for an ensemble forecast is defined as

\[\text{DSS}(F_{ens}, \mathbf{y})= (\mathbf{y} - \bar{mathbf{x}})^{\top} \Sigma^-1 (\mathbf{y} - \bar{mathbf{x}}) + \log \det(\Sigma)\]

where \(\bar{mathbf{x}}\) is the mean of the ensemble members (along each dimension), and \(\Sigma\) is the sample covariance matrix estimated from the ensemble members.

Parameters:

obsarray_like

The observed values, where the variables dimension is by default the last axis.

fctarray_like

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

m_axisint

The axis corresponding to the ensemble dimension. Defaults to -2.

v_axisint or tuple of int

The axis corresponding to the variables dimension. Defaults to -1.

biasbool

Logical specifying whether the biased or unbiased estimator of the covariance matrix should be used to calculate the score. Default is the unbiased estimator (bias=False).

backendstr

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

Returns:

score: Array

The computed Dawid-Sebastiani Score.