Bayesian variable selection via a benchmark in normal linear models

Jun Shao, Kam-Wah Tsui and Sheng Zhang

Statistical Theory and Related Fields, 2021, vol. 5, issue 1, 70-81

Abstract: With increasing appearances of high-dimensional data over the past two decades, variable selections through frequentist likelihood penalisation approaches and their Bayesian counterparts becomes a popular yet challenging research area in statistics. Under a normal linear model with shrinkage priors, we propose a benchmark variable approach for Bayesian variable selection. The benchmark variable serves as a standard and helps us to assess and rank the importance of each covariate based on the posterior distribution of the corresponding regression coefficient. For a sparse Bayesian analysis, we use the benchmark in conjunction with a modified BIC. We also develop our benchmark approach to accommodate models with covariates exhibiting group structures. Two simulation studies are carried out to assess and compare the performances among the proposed approach and other methods. Three real datasets are also analysed by using these methods for illustration.

Date: 2021
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DOI: 10.1080/24754269.2020.1744074

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