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Activity Number: 254 - Contributed Poster Presentations: Section on Bayesian Statistical Science
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #306397
Title: Fast Bayesian Variable Selection and FDR Control
Author(s): Su Chen* and Stephen Walker
Companies: The University of Texas At Austin and The University of Texas at Austin
Keywords: Bayesian variable selection; Spike and slab priors; Strong selection consistency; High dimensional data; Parallel computation; false discovery rate

We introduce a novel approach of Bayesian variable selection in the normal linear regression model with high dimensional data with both theoretical justification and fast parallel computation. An explicit posterior probability for including a covariate is obtained. The method is sequential but not order dependent, one deals with each covariate one by one, and a spike and slab prior is only assigned to the coefficient under investigation. We adopt the well-known spike and slab Gaussian priors with a sample size dependent variance, which achieves strong selection consistency for marginal posterior probabilities even when the number of covariates grows almost exponentially with sample size. We obtain the same results via the direct calculation of posterior probabilities, compared to a stochastic search over the entire model space. Our procedure also controls the False Discovery Rate under finite sample using posterior predictive p-value, loss functions and the approach of Benjamini and Hochberg.

Authors who are presenting talks have a * after their name.

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