Mechanistic hierarchical Gaussian processes.
Wheeler MW; Dunson DB; Pandalai SP; Baker BA; Herring AH
J Am Stat Assoc 2014 Sep; 109(507):894-904
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. Keywords:Functional data analysis; Gaussian process; Muscle force
Statistical-analysis; Mathematical-models; Muscles; Muscle-physiology; Physiological-stress; Physiology; Injuries; Animals; Laboratory-animals; Physical-exercise; Force; Analytical-processes; Models;
Author Keywords: Functional data analysis; Gaussian process; Muscle force; Ordinary differential
Matthew W. Wheeler, National Institute for Occupational Safety and Health 4676 Columbia Parkway, Cincinnati, Ohio 45226, MS C-15
Journal of the American Statistical Association