Abstract: In various fields, dependence between variables, which may be induced by time, space, biological networks, or other factors, is often observed. Incorporating this dependence structure has been shown to be important and can enhance the performance of variable selection. The Bayesian framework provides a natural way to integrate such information through suitable priors, which may be placed either on the variable selection indicators or directly on the regression coefficients.

In this talk, I will present two priors designed to enable the selection of structured variables. The first addresses graph-structured variables by combining a Gaussian Markov random field (MRF) prior with a global–local (GL) shrinkage prior. The second focuses on grouped variables that exhibit a serial structure within groups and performs a two-level selection.In the third part, in the context of disease propagation, I will introduce a non-stationary spatio-temporal model that provides a better understanding of disease spread in oil palm trees.

The proposed methods will be illustrated using simulated data and an application examining the impact of environmental variables on organ loss in oil palm.