PROPER LOCAL SCORING RULES ON DISCRETE SAMPLE SPACES
By By, Philip Dawid, Steffen L. Lauritzen, Matthew Parry. 2011
61 citations recorded by the source corpus.
A scoring rule is a loss function measuring the quality of a quoted probability distribution $Q$ for a random variable $X$, in the light of the realized outcome $x$ of $X$; it is proper if the expected score, under any distribution $P$ for $X$, is minimized by quoting $Q=P$. Using the fact that any differentiable proper scoring rule on a finite sample space ${\mathcal{X}}$ is the gradient of a concave homogeneous function, we consider when such a rule can be local in the sense of depending only on the probabilities quoted for points in a nominated neighborhood of $x$. Under mild conditions, we characterize such a proper local scoring rule in terms of a collection of homogeneous functions on the cliques of an undirected graph on the space ${\mathcal{X}}$. A useful property of such rules is that the quoted distribution $Q$ need only be known up to a scale factor. Examples of the use of such scoring rules include Besag's pseudo-likelihood and Hyv\"{a}rinen's method of ratio matching.
Subfields: Computational Theory and Mathematics, Economics and Econometrics, Statistics and Probability
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Citations in the corpus
- Theory and applications of proper scoring rules (2014, unknown): “Analogous results for discrete sample spaces have been given in [12], while somemultivariate extensions are considered in [25].”
- Strictly Proper Scoring Rules (2014, background): “The same authors transfer their extended notion of locality to finite discrete sample spaces in the companion paper [11].”