Bayesian bridge regression. Issue 6 (26th April 2018)

• Record Type: Journal Article
• Authors: Mallick, Himel; Yi, Nengjun
• Is Part Of: Journal of applied statistics. Volume 45:Issue 6(2018)
• Page Start: 988
• Page End: 1008
• Publication Date: 2018-04-26
• Subjects: Bayesian regularization -- bridge regression -- LASSO -- MCMC -- scale mixture of uniform -- variable selection; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2017.1324565
• Languages: English
• ISSNs: 0266-4763

Abstract

ABSTRACT: Classical bridge regression is known to possess many desirable statistical properties such as oracle, sparsity, and unbiasedness. One outstanding disadvantage of bridge regularization, however, is that it lacks a systematic approach to inference, reducing its flexibility in practical applications. In this study, we propose bridge regression from a Bayesian perspective. Unlike classical bridge regression that summarizes inference using a single point estimate, the proposed Bayesian method provides uncertainty estimates of the regression parameters, allowing coherent inference through the posterior distribution. Under a sparsity assumption on the high-dimensional parameter, we provide sufficient conditions for strong posterior consistency of the Bayesian bridge prior. On simulated datasets, we show that the proposed method performs well compared to several competing methods across a wide range of scenarios. Application to two real datasets further revealed that the proposed method performs as well as or better than published methods while offering the advantage of posterior inference.