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Activity Number: 23
Type: Topic Contributed
Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
Sponsor: International Society for Bayesian Analysis (ISBA)
Abstract #320809 View Presentation
Title: Standard Errors, Solution Paths, and Selection of Tuning Parameters for Bayesian Lassos
Author(s): Sounak Chakraborty* and Vivekananda Roy
Companies: University of Missouri - Columbia and Iowa State University
Keywords: Bayesian lasso ; elastic net ; geometric ergodicity ; importance sampling ; empirical Bayes ; standard errors

Penalized regression methods such as the lasso and elastic net (EN) have become popular for simultaneous variable selection and coefficient estimation. Implementation of these methods require selection of the penalty parameters. We propose an empirical Bayes (EB) methodology for selecting these tuning parameters as well as computation of the regularization path plots. The EB method does not suffer from the "double shrinkage problem" of frequentist EN. Also it avoids the difficulty of constructing an appropriate prior on the penalty parameters. The EB methodology is implemented by efficient importance sampling method based on multiple Gibbs sampler chains. Since the Markov chains underlying the Gibbs sampler are proved to be geometrically ergodic, Markov chain central limit theorem can be used to provide asymptotically valid confidence band for profiles of EN coefficients. The practical effectiveness of our method is illustrated by several simulation examples and three real life case studies. Although this article considers lasso and EN for brevity, the proposed EB method is general and can be used to select shrinkage parameters in other regularization methods.

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