  We propose a framework for fitting fractional polynomials models as special
cases of Bayesian Generalized Nonlinear Models, applying an adapted version of
the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The
universality of the Bayesian Generalized Nonlinear Models allows us to employ a
Bayesian version of the fractional polynomials models in any supervised
learning task, including regression, classification, and time-to-event data
analysis. We show through a simulation study that our novel approach performs
similarly to the classical frequentist fractional polynomials approach in terms
of variable selection, identification of the true functional forms, and
prediction ability, while providing, in contrast to its frequentist version, a
coherent inference framework. Real data examples provide further evidence in
favor of our approach and show its flexibility.
