Bayesian Trend Filtering

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Edward Roualdes*+
• Companies: University of Kentucky
• Keywords: trend filtering ; nonparametric regression ; Bayesian

Abstract

Trend filtering, as is being developed by Ryan J. Tibshirani and seen as a generalization of the 1d Fussed Lasso, nonparametrically estimates a univariate function by penalizing the (k+1)st discrete derivatives in a generalized lasso penalty form. Noting the connection between the lasso penalty and the Laplace prior, a fully Bayesian approach to trend filtering is presented. A hierarchical model is formed using a Laplace-like prior. A Gibbs sampler allows for fast estimation of the penalty parameter and credible intervals. This overcomes the well known poor performance of the bootstrap when coupled with super-efficient estimators such as the lasso. The similarities and differences between this Bayesian approach and the frequentist approach are highlighted.