Citation
Wheeler, Matthew W.; Dunson, David B.; Pandalai, Sudha P.; Baker, Brent A.; & Herring, Amy H. (2014). Mechanistic Hierarchical Gaussian Processes. Journal of the American Statistical Association, 109(507), 894-904. PMCID: PMC4273873Abstract
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 noninjurious 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.URL
http://dx.doi.org/10.1080/01621459.2014.899234Reference Type
Journal ArticleYear Published
2014Journal Title
Journal of the American Statistical AssociationAuthor(s)
Wheeler, Matthew W.Dunson, David B.
Pandalai, Sudha P.
Baker, Brent A.
Herring, Amy H.