Tractable Bayesian variable selection: beyond normality

Under suitable conditions misspecified Bayes factors induce sparsity at the same rates than under the correct model. However, the rates to detect signal change by an exponential factor, often reducing sensitivity. These deficiencies can be ameliorated by inferring the error distribution, a simple strategy that can improve inference substantially.

Our work focuses on the likelihood and can be combined with any likelihood penalty or prior, but here we focus on non-local priors to induce extra sparsity and ameliorate finite-sample effects caused by misspecification. We show the importance of considering the likelihood rather than solely the prior, for Bayesian variable selection. The methodology is in R package ‘mombf’.