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Assessing Predictive Performance: From Precipitation Forecasts over the Tropics to Receiver Operating Characteristic Curves and Back

Vogel, Peter

Abstract:
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. ... mehr

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Volltext §
DOI: 10.5445/IR/1000091649
Veröffentlicht am 26.02.2019
Coverbild
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Institut für Meteorologie und Klimaforschung - Forschungsbereich Troposphäre (IMK-TRO)
Publikationstyp Hochschulschrift
Jahr 2019
Sprache Englisch
Identifikator urn:nbn:de:swb:90-916493
KITopen-ID: 1000091649
Verlag KIT, Karlsruhe
Umfang X, 126 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Stochastik (STOCH)
Prüfungsdatum 06.02.2019
Referent/Betreuer Prof. T. Gneiting
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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