Disjunct Support Spike and Slab Priors for Variable Selection in Regression
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Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. Therefore, in practice, we may want to trade in a small reduction in prediction accuracy for an increase in sparseness. Spike-and-slab priors as introduced in (Chipman et al., 2001) can potentially handle such a trade-off between prediction accuracy and sparseness. However, here in this work, we show that spike-and-slab priors with full support lead to inconsistent Bayes factors, in the sense that the Bayes factors of any two models are bounded in probability. This is clearly an undesirable property for Bayesian hypotheses testing, where we wish that increasing sample sizes lead to increasing Bayes factors favoring the true model. As a remedy, we suggest disjunct support spike and slab priors, for which we prove consistent Bayes factors, and show experimentally fast growing Bayes factors favoring the true model. Several experiments on simulated and real data, confirm the usefulness of our proposed method to identify models with high effect size, while leading to better control over false positives than hard-thresholding.
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