Mechanistic Hierarchical Gaussian Processes

Details

• Alternative Title:
  J Am Stat Assoc
• Personal Author:
  Wheeler, Matthew W. ; Dunson, David B. ; Pandalai, Sudha P. ; Baker, Brent A. ; Herring, Amy H.
• Description:
  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 Ordinary Differential Equations Stochastic Differential Equations123
• Source:
  J Am Stat Assoc. 109(507):894-904
• Pubmed ID:
  25541568
• Pubmed Central ID:
  PMC4273873
• Document Type:
  Journal Article
• Funding:
  CC999999/ImCDC/Intramural CDC HHSUnited States/ ; P2C HD050924/HD/NICHD NIH HHSUnited States/ ; R01 ES017436/ES/NIEHS NIH HHSUnited States/ ; R01 ES020619/ES/NIEHS NIH HHSUnited States/
• Volume:
  109
• Issue:
  507
• Collection(s):
  CDC Public Access
• Main Document Checksum:
  urn:sha256:0b10096990cfdedb870216e101d26f4ba7804b9a6cb08a9ecd4a434606f8ec4a
• Download URL:
  https://stacks.cdc.gov/view/cdc/34821/cdc_34821_DS1.pdf
• File Type:
  [PDF - 651.00 KB ]