Energy score for multivariate forecasts — energy_score

Compute the energy score (Gneiting et al., 2008) for each multivariate group defined by mv_group_id. The energy score is a multivariate generalisation of the CRPS that measures both calibration and sharpness of the forecast distribution.

The score is computed using scoringRules::es_sample().

Usage

energy_score_multivariate(observed, predicted, mv_group_id, w = NULL)

Arguments

observed: A vector with observed values of size n
predicted: nxN matrix of predictive samples, n (number of rows) being the number of data points and N (number of columns) the number of Monte Carlo samples. Alternatively, if n = 1, predicted can just be a vector of size n.
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: Optional numeric vector of weights for forecast samples (length equal to the number of columns of predicted). If NULL (the default), equal weights are used.

Value

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

References

Gneiting, T., Stanberry, L.I., Grimit, E.P., Held, L. and Johnson, N.A. (2008). Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds. TEST, 17, 211-235.