Data augmentation for non-Gaussian regression models using variance-mean mixtures

We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme that unifies a wide class of statistical models under a single framework. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a much wider range of models than previously appreciated. We demonstate the resulting gains in accuracy and stability on several examples, including sparse quantile regression and binary logistic regression.