Some Priors for Sparse Regression Modelling

Abstract

A wide range of methods, Bayesian and others, tackle regression when there are many variables. In the Bayesian context, the prior is constructed to reflect ideas of variable selection and to encourage appropriate shrinkage. The prior needs to be reasonably robust to different signal to noise structures. Two simple evergreen prior constructions stem from ridge regression on the one hand and g-priors on the other. We seek to embed recent ideas about sparsity of the regression coefficients and robustness into these priors. We also explore the gains that can be expected from these differing approaches.