Bayesian Regression for High-Dimensional Data Using a Prior on the Model Fit

• Activity Number: 285 - Advances in Dimension Reduction and Model Selection for Statistically Challenging Data
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Howard D Bondell*
• Companies: University of Melbourne
• Keywords: Bayesian regression; Shrinkage prior; R-squared

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 conditional on the value of R-squared. In addition to a convenient interpretation, compared to existing shrinkage priors, we show that the use of this prior can provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals.