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Bayesian transformation family selection: Moving toward a transformed Gaussian universe
Author(s) -
Charitidou Efstratia,
Fouskakis Dimitris,
Ntzoufras Ioannis
Publication year - 2015
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11261
Subject(s) - transformation (genetics) , mathematics , skewness , markov chain monte carlo , posterior probability , power transform , bayesian probability , markov chain , statistical physics , econometrics , computer science , statistics , discrete mathematics , physics , biochemistry , chemistry , consistency (knowledge bases) , gene
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 λ T associated with each competing family T . We investigate different approaches to constructing compatible prior distributions for λ T 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 © 2015 Statistical Society of Canada