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Biometrika 1981 68(1):35-43; doi:10.1093/biomet/68.1.35
© 1981 by Biometrika Trust
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A Bayesian approach to transformations to normality

L. R. PERICCHI

Programa de Postgrado en Recursos Hidricos, Universidad Simon Bolivar Caracas, Venezuela

The analysis of transformation of observations in the linear model with normal errors proposed by Box & Cox (1964) is considered. A different choice of noninformative unnormed prior is advocated, which is not outcome dependent. This new selection of prior leads to a formal identity between likelihood and Bayesian inference, both for the estimation of the best transformation to normality and for the presence of homoscedasticity and additivity under this transformation. Extension to a related problem is mentioned.

Key Words: Jeffreys's multiparameter prior • Outcome-dependent prior • Posterior model odds • Transformation to normality


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