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Philip Dawid  (University of Cambridge, United Kingdom) (joint work with Matthew Parry and Steffen Lauritzen)
Monday, August 02, 2010, room Hörsaal 1
Local proper scoring rules

A scoring rule S(x, Q) measures the quality of a quoted distribution Q for an uncertain quantity X in the light of the realised value x of X. It is proper when it encourages honesty, i.e, when, if your uncertainty about X is represented by a distribution P, the choice Q = P minimises your expected loss. Traditionally, a scoring rule has been called local if it depends on Q only through q(x), the density of Q at x. The only proper local scoring rule is then the -score, . For the continuous case, we can weaken the definition of locality to allow dependence on a finite number m of derivatives of q at x. A full characterisation is given of such order-m local proper scoring rules, and their behaviour under transformations of the outcome space. In particular, any m-local scoring rule with m > 0 can be computed without knowledge of the normalising constant of the density. Parallel results for discrete spaces will be given.