Abstract

Proper scoring rules encourage honest assessment of personal probabilities. They can also be used to define general entropy functions, discrepancy functions, M-estimators, etc., and to extend composite likelihood methods.

When the sample space is a real interval, a proper scoring rule is termed local (of order m) if it depends only on the first m derivatives of the quoted density at the actually realised value. We have characterised all proper local scoring rules and shown that (excluding the log score) they can be computed without requiring the normalising constant of the density. This property is valuable for many purposes, including Bayesian model selection with improper priors.

Dawid, A. P. (1994) Proper Measures of Discrepancy Uncertainty and Dependence with Applications to Predictive Experimental Design.

Parry, M., Dawid, A. P. and Lauritzen, S. L. (2012). Proper local scoring rules. Ann. Statist. 40, 561-92.

Dawid, A. P. and Musio, M. (2012). Estimation of spatial processes using local scoring rules. Advances in Statistical Analysis. doi:10.1007/s10182-012-0191-8