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Biometrika 1990 77(1):107-114;
© 1990 by Biometrika Trust
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Articles

Data-translated likelihood and Jeifreys's rules

ROBERT E. KASS

Department of Statistics, Carnegie-Mellon University Pittsburgh, Pennsylvania 15213, U.S.A.

Received for publication 1 October 1988. Revision received 1 June 1989.
  Abstract

According to the definition used by Box & Tiao (1973) for a likelihood to be ‘data translated’ it must have location form in terms of a sufficient statistic. In contrast to Jeffreys's arguments for a uniform prior, theirs does not cover cases such as the Cauchy location family, and is in this sense stronger than the group-theoretic criterion of invariance. Their definition is easily modified to cover such cases through the introduction of an ancillary statistic, and their argument in favour of a uniform prior then becomes group-theoretic. Their concept of ‘approximate data-translated likelihood’ may also be modified to produce a sharper local approximation.

Key Words: Ancillary statistic • Information metric • Invariant prior • Reference prior


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