Adaptive Weight Function Estimation in Functional Linear Models via Fixed Form Variational Bayes

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Bruce Bugbee* and Jeffrey Morris and Veera Baladandayuthapani
• Companies: MD Anderson Cancer Center and MD Anderson Cancer Center and MD Anderson Cancer Center
• Keywords: Functional Data ; Variational Bayes ; Penalized Splines

Abstract

Functional linear models (FLM) are a common class of regression models used to incorporate functional covariates with scalar responses. Current methods typically estimate the coefficient weight function under global smoothness constraints, potentially missing local features. We extend the idea of using penalized splines with a spatially adaptive penalty term from nonparametric regression to functional linear models to address this problem. Additionally, we implement our model via fixed form variational Bayes, a computational approximation methodology that allows for fast, efficient calculation of posterior information. A detailed simulation study shows that our approach achieves better estimates of the weight function versus a global penalty method in cases where dramatic changes in curvature of the weight function are present. Adaptive penalization also leads to more informative uncertainty bands for the estimated weight function in many cases. Finally we highlight the advantages and difficulties associated with both global and adaptive FLMs in the context of genomics data associated with cancer research.