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Bayesian bridge regression
Authors:Himel Mallick  Nengjun Yi
Institution:1. Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA;2. Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, Cambridge, MA, USA;3. Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, USA
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
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