Mechanistic Hierarchical Gaussian Processes

• 成果类型: Article
• 署名作者: Wheeler, Matthew W.; Dunson, David B.; Pandalai, Sudha P.; Baker, Brent A.; Herring, Amy H.
• 署名单位: Centers for Disease Control & Prevention - USA; National Institute for Occupational Safety & Health (NIOSH); Duke University; Centers for Disease Control & Prevention - USA; National Institute for Occupational Safety & Health (NIOSH); University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.899234
• 发表日期: 2014
• 页码: 894-904
• 关键词: stretch-shortening contractions; skeletal-muscle force; chronic exposure; parameter-estimation; old rats; models; AGE; performance; SYSTEM; young

摘要

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.