Garthwaite, P. H.
Preposterior expected loss as a scoring rule for prior distributions.
Communications in Statistics - Theory and Methods, 21(12) pp. 3601–3619.
A scoring rule for evaluating the usefulness of an assessed prior distribution should reflect the purpose for which the distribution is to be used. In this paper we suppose that sample data is to become available and that the posterior distribution will be used to estimate some quantity under a quadratic loss function. The utility of a prior distribution is consequently determined by its preposterior expected quadratic loss. It is shown that this loss function has properties desirable in a scoring rule and formulae are derived for calculating the scores it gives in some common problems.
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