Compute the variogram score for multivariate point forecasts,
treating each point forecast as a single-sample ensemble.
This is a thin wrapper around
variogram_score_multivariate() with w = NULL.
See variogram_score_multivariate() for details on the
variogram score and its parameters.
variogram_score_multivariate_point(
observed,
predicted,
mv_group_id,
w_vs = NULL,
p = 0.5
)A named numeric vector of scores, one per multivariate group. Lower values are better.
A vector with observed values of size n
Numeric matrix with one column, where each row corresponds to a target within a multivariate group.
Numeric vector of length n with ids indicating the
grouping of predicted values. Conceptually, each row of the predicted
matrix could be seen as a separate (univariate) forecast.
The grouping id then groups several of those forecasts together, treating
them as a single multivariate forecast.
Optional non-negative weight matrix for the
pairwise comparisons between targets. Entry w_vs[i, j]
controls the importance of the pair (i, j) in the score.
Must be a symmetric square matrix with rows and columns
equal to the number of targets within each multivariate
group.
If NULL (the default), all pairs are weighted equally.
Numeric, order of the variogram score. This controls
how pairwise differences are scaled: the score compares
|y_i - y_j|^p across targets. Lower values of p give
less weight to large differences, making the score more
robust to outliers. Typical choices are 0.5 (the default)
and 1.
Scheuerer, M. and Hamill, T.M. (2015). Variogram-Based Proper Scoring Rules for Probabilistic Forecasts of Multivariate Quantities. Monthly Weather Review, 143, 1321-1334.