Objective Bayesian transformation and variable selection using default Bayes factors

• Published in: Statistics and computing Vol. 28; no. 3; pp. 579 - 594
• Main Authors: Charitidou, E., Fouskakis, D., Ntzoufras, I.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2018; Springer Nature B.V
• Subjects: Artificial Intelligence; Bayesian analysis; Mathematics and Statistics; Probability and Statistics in Computer Science; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Transformations; Bayesian model selection; Intrinsic Bayes factor; Fractional Bayes factor; Transformation family selection; Posterior model probabilities; Variable selection
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-017-9749-3

In this work, the problem of transformation and simultaneous variable selection is thoroughly treated via objective Bayesian approaches by the use of default Bayes factor variants. Four uniparametric families of transformations ( Box–Cox , Modulus , Yeo-Johnson and Dual ), denoted by T , are evaluated and compared. The subjective prior elicitation for the transformation parameter λ T , for each T , is not a straightforward task. Additionally, little prior information for λ T is expected to be available, and therefore, an objective method is required. The intrinsic Bayes factors and the fractional Bayes factors allow us to incorporate default improper priors for λ T . We study the behaviour of each approach using a simulated reference example as well as two real-life examples.