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Description:
Educated decision making involves two major ingredients: probabilistic forecasts for future events or quantities and an assessment of predictive performance. This thesis focuses on the latter topic and illustrates its importance and implications from both theoretical and applied perspectives. Receiver operating characteristic (ROC) curves are key tools for the assessment of predictions for binary events. Despite their popularity and ubiquitous use, the mathematical understanding of ROC curves is still incomplete. We establish the equivalence between ROC curves and cumulative distribution functions (CDFs) on the unit interval and elucidate the crucial role of concavity in interpreting and modeling ROC curves. Under this essential requirement, the classical binormal ROC model is strongly inhibited in its flexibility and we propose the novel beta ROC model as an alternative. For a class of models that includes the binormal and the beta model, we derive the large sample distribution of the minimum distance estimator. This allows for uncertainty quantification and statistical tests of goodness-of-fit or equal predictive ability. Turning to empirical examples, we analyze the suitability of both models and find empirical evidence for the increased flexibility of the beta model. A freely available software package called betaROC is currently prepared for release for the statistical programming language R. Throughout the tropics, probabilistic forecasts for accumulated precipitation are of economic importance. However, it is largely unknown how skillful current numerical weather prediction (NWP) models are at timescales of one to a few days. For the first time, we systematically assess the quality of nine global operational NWP ensembles for three regions in northern tropical Africa, and verify against station and satellite-based observations and for the monsoon seasons 2007-2014. All examined NWP models are uncalibrated and unreliable, in particular for high probabilities of precipitation, and underperform in the ...