The geometry of proper scoring rules

By A. P. Dawid. 2007

196 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics, Statistics and Probability, Information Theory

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Citations in the corpus

Proper local scoring rules (2011, background): “ed (separable) Bregman scoring rule is deﬁned by S(x,Q):=φ′{q(x)}+ Z (3) dµ(y)[φ{q(y)}−q(y)φ′{q(y)}]. It can be shown that these are the only proper scoring rules having the form S(x,Q)=ξ{q(x)}−k(Q) [Dawid (2007)]. Taking expectations, we obtain S(P,Q)= Z dµ(x)[{p(x)−q(x)}φ′{q(x)}+φ{q(x)}]. It follo”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, background): “Details of the construction are given in section 3 of Dawid (2007) and section 2.2 of Gneiting and Raftery (2007).)”
Cramer-Rao Lower Bound and Information Geometry (2013, background): “To illustrate the versatility of information geometry, let us mention a few research areas: • Fisher-Rao Riemannian geometry [37], • Amari’s dual connection information geometry [6], • Infinite-dimensional exponential families and Orlicz spaces [16], • Finsler information geometry [45], • Optimal tr”
NGBoost: Natural Gradient Boosting for Probabilistic Prediction (2019, background): “The MLE scoring rule induces the Kullback-Leibler divergence (KL divergence, or DKL), while CRPS induces the L2 divergence (Dawid, 2007; Machete, 2013).”
Local Proper Scoring Rules (2009, background): “It will be convenient to define an equivalence relation for scoring rules (Dawid 2007).”
Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction (2012, background): “Optimum score estimation returns unbiased parameter estimates (Dawid, 2007), and for the ignorance score, this equals maximum likelihood estimation for independent observations.”
Composite Multiclass Losses (2011, background): “Minimaxity of proper losses has been studied in a very general setting by Grünwald and Dawid (2004) who showed the connection between robust Bayes procedures and maximum entropy; confer classical results presented, for example, by Ferguson (1967).”
Local proper scoring rules of order two (2011, background): “The term proper was coined by Winkler and Murphy (1968), while the general idea can be traced to Brier (1950) and Good (1952).”
Theory and applications of proper scoring rules (2014, background): “In particular, the whole theory of information geometry, which subsumes but goes beyond the information metric on P , can be generalised to yield the decision geometry associated with a given PSR (Dawid and Lauritzen 2005; Dawid 2007).”
Minimum Scoring Rule Inference (2014, background): “There is a very wide variety of proper scoring rules: for general characterisations see, among others, McCarthy (1956), Savage (1971), and for various special cases see Dawid (1998, 2007) and Gneiting and Raftery (2007).”
Information, Divergence and Risk for Binary Experiments (2009, background): “…distance minimisation (Borwein and Lewis, 1991; Altun and Smola, 2006; Broniatowski, 2004), and more narrowly focussed “unifying frameworks” such as information geometry (Dawid, 2007; Eguchi, 2005), exponential families (Canu and Smola, 2006) and the information bottleneck (Tishby et al., 2000).”