A1436
Title: Model comparison for Bayesian lasso-like regression
Authors: Christopher Hans - The Ohio State University (United States) [presenting]
Ningyi Liu - The Ohio State University (United States)
Abstract: Formal Bayesian methods for model comparison depend on the marginal likelihood of the data given a model. When closed-form expressions for marginal likelihoods in a given model class are not available, it is common to employ computational approaches to either estimate the marginal likelihoods directly or to avoid their explicit evaluation by summarizing output from carefully constructed MCMC algorithms. While Bayesian treatments of approaches to penalized regression have become popular tools for data analysis, formal Bayesian model comparison in these settings can be challenging. Computing marginal likelihoods for Bayesian lasso-like regression models is difficult due to the L1-norm penalty term that is incorporated into the prior on the regression coefficients. MCMC-based approaches are introduced for estimating the marginal likelihoods for the Bayesian lasso and elastic net regression models. The methods involve sampling from standard probability distributions, need not rely on any data augmentation, and require no tuning of random walks or specification of approximating distributions. Comparisons are made to other related approaches for marginal likelihood estimation.
