Statistical methods for probabilistic forecasts of real-valued outcomes

The work considers three essential steps to properly perform a forecasting task where the target variable is real-valued and the corresponding forecasts are probabilistic. The three steps involve data analysis, fitting a model and forecast evaluation.

For binary target variables, there exist various methods to properly perform each of the forecasting steps while for continuous data the set of possible approaches is considerably smaller. To overcome this shortcoming, three new tools are presented which are either extensions of binary approaches or motivated by their binary counterpart.

First, a natural extension of classical ROC analysis is presented in the form of ROC movies, UROC curve and CPA. Then EasyUQ and smooth EasyUQ are introduced which produce calibrated statistical forecast distributions based on real-valued model output. Finally, a CRPS decomposition is proposed to obtain more informative components for forecast evaluation. In the last chapter of this thesis, the new tools are successively applied to a challenge weather forecasting problem, namely producing probabilistic forecasts for accumulated precipitation over the tropics.