Bayesian Hierarchical Feature Selection of Structured Functional Predictors for Multilevel Functional Data Measured with Error

• Activity Number: 297
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yize Zhao*+ and Jian Kang and Qi Long
• Companies: Emory University and Emory University and Emory University, Department of Biostatistics
• Keywords: Gaussian process ; Generalized functional linear models ; Hierarchical feature selection ; Ising prior ; Markov chain Monte Carlo ; Measurement error

Abstract

In this paper, we propose a unified Bayesian approach for hierarchical feature selection of structured functional predictors in Generalized Functional Linear Models (GFLMs), which also accommodates multi-level functional data and measurement error. Feature selection of functional predictors in GFLMs is inherently hierarchical, involving selection of functional predictors and selection of regions within each functional predictor. To achieve such feature selection, we construct a class of mixture priors for functional coefficients based on modified Gaussian processes. We use Ising priors on the model space to incorporate two levels of structural information: between functional predictors and within each functional predictor. Our approach also incorporates a hierarchical Gaussian process model for multilevel functional data that are measured with error. We apply our methods to a recent colorectal adenoma study and find that one functional biomarker and its expression level in the transitional region between the proliferation and differentiation zones are associated with the risk for colorectal cancer. The performance of our methods is also illustrated in simulation studies.