Display options
Cite
Wheeler MW, Dunson DB, Pandalai SP, et al. Mechanistic Hierarchical Gaussian Processes. J Am Stat Assoc. 2014;109(507):894-904doi: 10.1080/01621459.2014.899234.
Wheeler, M. W., Dunson, D. B., Pandalai, S. P., Baker, B. A., & Herring, A. H. (2014). Mechanistic Hierarchical Gaussian Processes. Journal of the American Statistical Association, 109(507), 894-904. https://doi.org/10.1080/01621459.2014.899234
Wheeler, Matthew W, et al. "Mechanistic Hierarchical Gaussian Processes." Journal of the American Statistical Association vol. 109,507 (2014): 894-904. doi: https://doi.org/10.1080/01621459.2014.899234
Wheeler MW, Dunson DB, Pandalai SP, Baker BA, Herring AH. Mechanistic Hierarchical Gaussian Processes. J Am Stat Assoc. 2014 Jul;109(507):894-904. doi: 10.1080/01621459.2014.899234. PMID: 25541568; PMCID: PMC4273873.
Copy Download .nbib Format: NLM
Share it on

J Am Stat Assoc. 2014 Jul;109(507):894-904. doi: 10.1080/01621459.2014.899234.

Mechanistic Hierarchical Gaussian Processes.

Journal of the American Statistical Association

Matthew W Wheeler, David B Dunson, Sudha P Pandalai, Brent A Baker, Amy H Herring

Affiliations

  1. National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, Ohio 45226, MS C-15.
  2. Department of Statistical Science, Duke University.
  3. Department of Biostatistics, University of North Carolina at Chapel Hill.

PMID: 25541568 PMCID: PMC4273873 DOI: 10.1080/01621459.2014.899234

Abstract

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 equations

References

  1. Interface Focus. 2011 Dec 6;1(6):821-35 - PubMed
  2. Exp Gerontol. 2006 Apr;41(4):398-406 - PubMed
  3. Eur J Appl Physiol. 2010 Feb;108(3):619-30 - PubMed
  4. IEEE Trans Pattern Anal Mach Intell. 2013 Nov;35(11):2693-705 - PubMed
  5. J Gerontol A Biol Sci Med Sci. 2008 Oct;63(10):1015-26 - PubMed
  6. Appl Physiol Nutr Metab. 2006 Oct;31(5):573-87 - PubMed
  7. BMC Syst Biol. 2012 May 30;6:53 - PubMed
  8. J Pharmacokinet Pharmacodyn. 2002 Jun;29(3):271-307 - PubMed
  9. Bioinformatics. 2008 Mar 15;24(6):833-9 - PubMed
  10. Proc Natl Acad Sci U S A. 2010 Apr 27;107(17 ):7793-8 - PubMed
  11. Stat Med. 2002 Aug 15;21(15):2199-214 - PubMed
  12. Eur J Appl Physiol. 2010 Sep;110(2):223-34 - PubMed
  13. J Comput Biol. 2006 Apr;13(3):838-51 - PubMed
  14. Biometrics. 2006 Jun;62(2):413-23 - PubMed
  15. Eur J Appl Physiol. 2010 Feb;108(3):589-97 - PubMed
  16. J Am Stat Assoc. 2011 Dec 1;106(496):1485-1495 - PubMed
  17. Hum Mov Sci. 2004 Nov;23(5):591-604 - PubMed
  18. Appl Physiol Nutr Metab. 2007 Jun;32(3):443-53 - PubMed
  19. Comput Biol Med. 2004 Jun;34(4):307-22 - PubMed
  20. Interface Focus. 2011 Dec 6;1(6):807-20 - PubMed
  21. J Appl Physiol (1985). 1998 Dec;85(6):2176-89 - PubMed
  22. Biomed Mater Eng. 2006;16(6):369-80 - PubMed
  23. Med Eng Phys. 2011 Jun;33(5):581-9 - PubMed
  24. Bioinformatics. 2008 Aug 15;24(16):i70-5 - PubMed
  25. IEEE Trans Biomed Eng. 1997 May;44(5):337-48 - PubMed

Publication Types

Grant support