B0825
Title: Sampling the Bayesian elastic net
Authors: Christopher Hans - The Ohio State University (United States) [presenting]
Ningyi Liu - The Ohio State University (United States)
Abstract: The Bayesian elastic net regression model is characterized by the prior distribution of the regression coefficients, the negative log density of which corresponds to the elastic net penalty. The simplest MCMC methods for posterior sampling use data augmentation to expand the parameter space, yielding a Gibbs sampling update for the regression coefficients at the expense of additional sampling steps for the latent variables. Other direct sampling methods eschew the latent variables and update the regression coefficients one at a time. Under both approaches, sampling the remaining model parameters is complicated by an intractable (though numerically computable) integral in the prior normalizing constant. Sampling methods have been proposed that avoid the need to compute the normalizing constant. Still, the correctly specified methods described in the literature involve at least one Metropolis step, requiring specification and tuning of proposal distributions. Two new approaches are introduced for sampling that allow for direct sampling from all full conditionals with low computational cost. The approaches are compared to other existing methods.
