The quadratic scoring rule as a basis for experiment comparision

Abstract

In this paper, the role of strictly proper quadratic utility measures in Bayesian inference and experiment comparison is investigated. This utility function, which is not local, provides a good basis for the resolution of many real situations which are not purely inferential. By recognizing the decision problem underlying statistical inference, we obtain the criteria for experiment comparison based on the quadratic scoring rule. Properties and relations with other criteria are studied, particularly with those based on sufficiency and on the maximation of the informational energy gain. Finally some particular cases are commented and new areas of research suggested.