Bayesian Generalized ANOVA Modeling for Functional Data Using INLA

• Activity Number: 665
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yu Yue* and David Bolin and Havard Rue and Xiao-feng Wang
• Companies: Baruch College and Chalmers University of Technology and Norwegian University of Science and Technology and Cleveland Clinic Lerner Research Institute
• Keywords: functional data ; generalized ANOVA ; integrated nested Laplace approximations ; Gaussian Markov random fields ; contour avoiding functions ; Bayesian inference

Abstract

Functional analysis of variance (ANOVA) modeling has been proved particularly useful to investigate the dynamic changes of functional data according to certain categorical factors and their interactions. However, the current existing methods often encounter difficulties when the functional data are high-dimensional, non-Gaussian, and/or exhibit certain shape characteristics that vary with spatial locations. In this paper, we propose a unified generalized functional ANOVA modeling approach under Bayesian framework. The models are constructed based on a class of highly flexible Gaussian Markov random fields (GMRFs) taken on the effect functions as priors. This allows us to consider various types of functional effects, such as (discrete or continuous) temporal effects and (point-level or areal) spatial effects. The posterior distributions are obtained by an efficient computational tool based on integrated nested Laplace approximations (INLA) (Rue et al., 2009). We also employ the excursion method (Bolin and Lindgren, 2015) to build simultaneous credible intervals of functional effects and test their significance from a Bayesian point of view.