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BAYESIAN PRIORS BASED ON A PARAMETER

TRANSFORMATION USING THE DISTRIBUTION FUNCTION

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MARTIN CROWDER

*Department of Mathematical and Computing Sciences,*

University of Surrey, Guildford, Surrey, GU2 5XH, U.K.
(Received January 30, 1989; revised May 20, 1991)

**Abstract.**
One of the tasks of the Bayesian consulting
statistician is to
elicit prior information from his client who may be unfamiliar with parametric
statistical models. In some cases it may be more illuminating to base a prior
distribution for parameter *theta* on the transformed version
*F*(*v*|*theta*), where
*F* is the data distribution function and *v* is a designated reference
value, rather
than on *theta* directly. This approach is outlined and explored in various
directions to assess its implications. Some applications are given, including
general linear regression and transformed linear models.

*Key words and phrases*:
Bayesian priors, priors for location-scale
regression models, priors for transformed linear models, proper priors.

**Source**
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