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SUMMARY:Predictive evaluation of extremes and related functionals - Thordi
 s Thorarinsdottir (University of Oslo)
DTSTART:20250529T093000Z
DTEND:20250529T103000Z
UID:TALK231730@talks.cam.ac.uk
DESCRIPTION:Predicting future outcomes is one of the fundamental goals of 
 statistical analysis. Predictions for events with significant inherent unc
 ertainty should be probabilistic in nature to convey information on the un
 certainty associated with the outcome.&nbsp\; This is particularly of impo
 rtance when the prediction problems involves the prediction of a risk meas
 ure or a functional of the outcome distribution. For extreme events or ris
 ks\, the evaluation of the prediction falls in three distinct categories\,
  depending on the question being asked:\n\nA probabilistic forecast is iss
 ued for the extremes only and we want to know how good it is\;\nA probabil
 istic forecast is issued for every type of outcome\, and we want to know h
 ow good it is at predicting extreme outcomes\;\nA probabilistic forecast i
 s issued for every type of outcome\, and we want to know how well certain 
 tail properties or functionals of the predictive distribution match those 
 of the true data distribution.\n\nWhen predicting extreme events and asses
 sing risk\, the evaluation of the forecasts is additionally complicated by
  a lack of substantial observation set due to the rarity of the outcome of
  interest. We discuss how to perform the evaluation for all three categori
 es above under these constraints within the frameworks of proper scoring r
 ules and consistent scoring functions.&nbsp\; For functional predictions\,
  a well-matched scoring function may not exist as is the case\, for exampl
 e\, for the variance functional\, making the functional non-elicitable. Fo
 r this case\, we present some new results that show that non-elicitibility
  of the predicted functional may be solved by instead evaluating against t
 he observed\, or the estimated\, functional rather than observed outcomes 
 if sufficient data is available.
LOCATION:Seminar Room 2\, Newton Institute
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