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Biometrika 1984 71(1):127-134; doi:10.1093/biomet/71.1.127
© 1984 by Biometrika Trust
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On the choice of prior distribution for the Box-Cox transformed linear model

TREVOR J. SWEETING

Department of Mathematics, University of Surrey Guildford, U.K.

The noninformative prior distribution for the parameters of the linear model transformed following Box & Cox (1964) has the non-Bayesian property of depending to some extent on the data. An alternative choice of prior which is not outcome-dependent was suggested by Pericchi (1981), but it is argued here that this prior has some undesirable features. An alternative family of non-outcome-dependent priors is suggested, leading to a noninformative prior which is closer in spirit to that proposed by Box & Cox. The posterior consequences of adopting this prior are fully explored, and an example discussed.

Key Words: Box-Cox transformation • Marginalization paradox • Outcome-dependent prior


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