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Partial information reference priors: derivation and interpretations

✍ Scribed by B. Clarke; A. Yuan

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 406 KB
Volume: 123
Category: Article
ISSN: 0378-3758
DOI: 10.1016/s0378-3758(03)00157-5

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✦ Synopsis

Suppose X1; : : : ; Xn are IID p(•|Â; ) where (Â; ) ∈ R d is distributed according to the prior density w(•). For estimators Sn =S(X ) and Tn =T (X ) assumed to be consistent for some function of Â and asymptotically normal, we examine the conditional Shannon mutual information (CSMI) between and Tn given and Sn, I ( ; Tn| ; Sn). It is seen there are several important special cases of this CSMI. We establish asymptotic formulas for various cases and identify the resulting noninformative reference priors. As a consequence, we develop the notion of data-dependent priors and a calibration for how close an estimator is to su ciency.

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