Bayesian transformation family selection: Moving toward a transformed Gaussian universe

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 & 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 AT associated with each competing family T. We investigate different approaches to constructing compatible prior distributions for AT over alternative transformation families Selection and discrimination between different transformation families are attained via posterior model probabilities. Although there is no choice of transformation family that can be universally applied to all problems, empirical evidence suggests that some particular data structures are best treated by specific transformation families For example, skewness is associated with the Box Cox family while fat-tailed distributions are efficiently treated using the Modulus transformation. The Canadian Journal of Statistics 43: 600-623; 2015 (C) 2015 Statistical Society of Canada