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Activity Number: 55 - Advances in Bayesian Sparse Regression
Type: Contributed
Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #313221
Title: Model Based Screening Embedded Bayesian Variable Selection for Ultra-High-Dimensional Settings
Author(s): Dongjin Li* and Somak Dutta and Vivekananda Roy
Companies: Iowa State University and Iowa State University and Iowa State University
Keywords: Bayesian variable selection; ultra-high dimension ; spike and slab; prediction intervals; scalable algorithm
Abstract:

We propose a model based screening embedded Bayesian variable selection method in ultra-high dimensional settings where the number of predictors grows nearly exponentially with the sample size. The proposed approach, called BSVS, is developed based on a hierarchical model with priors placed on the regression coefficients as well as on the model space. Gaussian spike and slab prior is placed on the coefficients for important variables, making the posterior probability of a model available in explicit form. We prove that our method attains strong model selection consistency even when the coefficients corresponding to the inactive covariates diverge, which is an attractive feature not demonstrated by any other variable selection method in the literature. An appealing byproduct of BSVS is the construction of the first ever model weight adjusted prediction intervals. Using fast Cholesky updates we propose a dramatically scalable algorithm to rapidly explore the large model space and identify the regions of high posterior probabilities. The performance of the method is demonstrated through a number of simulation experiments and a real data example with over half a million variables.


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