title: Mechanistic Hierarchical Gaussian Processes.
abstract: The statistics literature on functional data analysis focuses primarily on flexible black-box approaches, which are designed to allow individual curves to have essentially any shape while characterizing variability. Such methods typically cannot incorporate mechanistic information, which is commonly expressed in terms of differential equations. Motivated by studies of muscle activation, we propose a nonparametric Bayesian approach that takes into account mechanistic understanding of muscle physiology. A novel class of hierarchical Gaussian processes is defined that favors curves consistent with differential equations defined on motor, damper, spring systems. A Gibbs sampler is proposed to sample from the posterior distribution and applied to a study of rats exposed to non-injurious muscle activation protocols. Although motivated by muscle force data, a parallel approach can be used to include mechanistic information in broad functional data analysis applications.
authors.affiliation: National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, Ohio 45226, MS C-15.
authors.forename: Matthew W
authors.initials: MW
authors.lastname: Wheeler
authors.affiliation: Department of Statistical Science, Duke University.
authors.forename: David B
authors.initials: DB
authors.lastname: Dunson
authors.affiliation: National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, Ohio 45226, MS C-15.
authors.forename: Sudha P
authors.initials: SP
authors.lastname: Pandalai
authors.affiliation: National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, Ohio 45226, MS C-15.
authors.forename: Brent A
authors.initials: BA
authors.lastname: Baker
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill.
authors.forename: Amy H
authors.initials: AH
authors.lastname: Herring
keywords: Functional data analysis; Gaussian process; Muscle force; Ordinary differential equations; Stochastic differential equations