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Activity Number: 332 - SPEED: Section on Bayesian Statistical Science
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #324042
Title: Dynamic Posterior Exploration for Simultaneous Variable and Covariance Selection with Spike and Slab Priors
Author(s): Sameer Kirtikumar Deshpande* and Veronika Rockova and Edward I. George
Companies: The Wharton School and University of Chicago and Wharton, University of Pennsylvania
Keywords: Multivariate Regression ; Gaussian Graphical Models ; Bayesian Penalty Mixing ; Expectation-Maximization ; Bayesian Variable Selection
Abstract:

We propose a Bayesian procedure for simultaneous variable and covariance selection with continuous spike-and-slab priors in high-dimensional multivariate linear regression models where q possibly correlated response are regressed onto a pool of p predictors. Rather than relying on a stochastic search through the 2^pq-dimensional model space, we deploy an EM algorithm similar to the EMVS procedure of Rockova and George (2014) to identify the posterior mode of the regression coefficients and precision matrix. Varying the scale of the continuous spike density facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial correlations gradually. We discuss natural ways to incorporate "structured sparsity" among the regression coefficients into this framework and demonstrate our methodology with simulated and real-world examples.


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