On Bayesian Transformation Selection: Problem Formulation and Preliminary Results

Abstract

The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo and Johnson and the Dual transformation. Markov Chain Monte Carlo algorithms have been constructed in order to sample from the posterior distribution of the transformation parameter λ _T associated with each competing family T. We investigate different approaches to constructing compatible prior distributions for λ _T over alternative transformation families, using the power-prior and the unit-information prior approaches. In order to distinguish between different transformation families, posterior model probabilities have been calculated. Using simulated datasets, we show the usefulness of our approach.