Bayesian bridge regression

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.

KEYWORDS:

• Bayesian regularization
• bridge regression
• LASSO
• MCMC
• scale mixture of uniform
• variable selection

Acknowledgements

We thank the associate editor and the two anonymous reviewers for their helpful comments. This work was supported in part by the research computing resources acquired and managed by University of Alabama at Birmingham IT Research Computing. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the University of Alabama at Birmingham.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Himel Mallick http://orcid.org/0000-0003-4956-2429.

Additional information

Funding

Himel Mallick was supported in part by the National Institute of Neurological Disorders and Stroke (research grant number U01 NS041588) and National Science Foundation (research grant number 1158862). Nengjun Yi was supported in part by the National Institutes of Health (research grant number 5R01GM069430-08).