A hybrid deterministic-deterministic approach for high-dimensional Bayesian variable selection with a default prior

Identifying relevant variables among numerous potential predictors has been of primary interest in modern regression analysis. While stochastic search algorithms have surged as a dominant tool for Bayesian variable selection, when the number of potential predictors is large, their practicality is constantly challenged due to high computational cost as well as slow convergence. In this paper, we propose a new Bayesian variable selection scheme by using hybrid deterministic-deterministic variable selection (HD-DVS) algorithm that asymptotically ensures a rapid convergence to the global mode of the posterior model distribution. A key feature of HD-DVS is that it allows us to circumvent the iterative computation of inverse matrices, which is a common computational bottleneck in Bayesian variable selection. A simulation study is conducted to demonstrate that our proposed method outperforms existing Bayesian and frequentist methods. An analysis of the Bardet-Biedl syndrome gene expression data is presented to illustrate the applicability of HD-DVS to real data.