A Measure of Local Sensitivity for Proper Scoring Rules in a Bayesian Setting
MUSIO, MONICA
2011-01-01
Abstract
Suppose to express the uncertainty about an unobserved quantity $X \in \mathcal{X}$ by quoting a distribution $Q$ over $\mathcal{X}$, after which Nature reveals the value $x$ of $\mathcal{X}$. A {\em Scoring Rule} e $S(x, Q)$ provides a way of judging the quality of a quoted probability distribution $Q$ for in the light of its outcome $x$. It is called proper if honesty is your best policy, i.e. when you believe X has distribution P in M, your expected score is optimized by the choice Q=P. Every statistical decision problem induces a proper scoring rule. In this work we propose a general definition of local sensitivity index for Proper Scoring Rules from a Bayesian decision point of view. We show as this new index is an intrinsic characteristic of the class M.Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.