Mechanistic Hierarchical Gaussian Processes

作者：Wheeler Matthew W^*; Dunson David B; Pan***** Sudha P; Baker Brent A; Herring Amy H

来源：Journal of the American Statistical Association, 2014, 109(507): 894-904.

DOI：10.1080/01621459.2014.899234

• Muscle force
• Gaussian process
• Ordinary differential equations
• Stochastic differential equations
• Functional data analysis

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.

• 出版日期2014-7-3