The energy distance for ensemble and scenario reduction

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy power systems, but also used probabilistic forecasting, clustering estimating generative adversarial networks. We propose a new method ensemble scenario based on the distance which is special case of maximum mean discrepancy. discuss choice detail, comparison to popular Wasserstein dominating literature. The metric between probability measures that allows powerful tests equality arbitrary multivariate distributions or independence. Thanks latter, it suitable candidate problems. theoretical properties considered examples indicate clearly reduced sets tend exhibit better statistical than corresponding with respect distance. show applications Bernoulli random walk two real data-based electricity demand profiles day-ahead prices. This article part theme issue ‘The mathematics systems’.