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Activity Number: 477 - Bayesian Methods for High-Dimensional Inference
Type: Invited
Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #323733 View Presentation
Title: High-Dimensional Linear Regression via the R-Squared Induced Dirichlet Decomposition Prior
Author(s): Howard Bondell* and Brian Reich and Yan Dora Zhang
Companies: NC State University and NCSU and Johns Hopkins
Keywords:
Abstract:

We introduce a new class of prior distributions for linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression R-squared. This is then distributed to the coefficients by decomposing it via a Dirichlet Distribution. We call the new prior R2-D2 in light of its R-Squared Dirichlet Decomposition. Compared to existing shrinkage priors, we show that the R2-D2 prior can simultaneously achieve both high prior concentration at zero, as well as heavier tails. These two properties combine to provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals.


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