Printed in Great Britain On the choice of prior distribution for the Box-Cox transformed linear model

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 sug-gested, 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. Some key xoords: Box-Cox transformation; Marginalization paradox; Outcome-dependent prior. 1