Variogram score for multivariate point forecasts — variogram_score_multivariate

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.

Usage

variogram_score_multivariate_point(
  observed,
  predicted,
  mv_group_id,
  w_vs = NULL,
  p = 0.5
)

Arguments

observed: A vector with observed values of size n
predicted: Numeric matrix with one column, where each row corresponds to a target within a multivariate group.
mv_group_id: 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.
w_vs: 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.
p: 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.

Value

A named numeric vector of scores, one per multivariate group. Lower values are better.

References

Scheuerer, M. and Hamill, T.M. (2015). Variogram-Based Proper Scoring Rules for Probabilistic Forecasts of Multivariate Quantities. Monthly Weather Review, 143, 1321-1334.