On variable selection with non-linear effects

G. García-Donato, R. Paulo

Traditional variable selection assumes that the effect on the mean response of each of the p potential
explanatory variables is linear. From a Bayesian model selection point of view, this can be addressed
by comparing the 2^p models via posterior model probabilities and computing the ensuing posterior
inclusion probabilities of each variable. We enlarge this model space by allowing the possibility that
the effect of each variable is non-linear, which we model via a Gaussian process. This results in a
model space containing 3p competing models: each predictor is either inactive, has a linear effect, or
has a non-linear effect. In this talk, we discuss various aspects of implementing such a strategy,
including computation, prior specification for the parameters specifying the covariance function of
the Gaussian processes, and on the model space.

Keywords: Bayes factors, Laplace approximation, Prior model probabilities

GT Inferencia Bayesiana
September 5, 2026  4:00 PM
Aula 20

C. Ausin, A. Sarhadi, M. P. Wiper

Á. Berihuete Macías, L. González Ramírez, J. Olivares Romero, L. M. Sarro Baro, D. Barrado Navascués

M. Rodríguez Rosa, M. Anciones Polo

C. García Meixide, D. Ríos Insua