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Cardiovascular Engineering

, Volume 8, Issue 2, pp 135–143 | Cite as

Statistical Considerations and Techniques for Understanding Physiological Data, Modeling, and Treatments

  • Ben G. Fitzpatrick
Original Paper

Abstract

Comparing models with data always forces us to deal with uncertainty. This uncertainty may take many different forms and involve multiple scales of resolution in the model and in the experiment. In this paper, we discuss issues surrounding the development of deterministic dynamic models of mean behavior and the associated statistical models of the difference between model and experiment. We touch on a variety of topics, including basic exploratory data analysis, confidence bounds and model reduction hypothesis tests. Tools ranging from nonlinear regression to time series to Bayesian decision theory are presented.

Keywords

Statistics Bayesian analysis Nonlinear regression 

Notes

Acknowledgments

We are grateful to the American Institute for Mathematics for hosting the Workshop on Short-Term Cardiovascular-Respiratory Control Mechanisms, at which this material was presented. We are especially grateful to Professors Jerry Batzel, Ary Goldberger, Franz Kappel, Johnny Otteson, Mette Olufsen, Vladimir Protopopescu, and Hien Tran for many stimulating and illuminating discussions during the workshop.

References

  1. Banks HT, Fitzpatrick BG. Statistical tests for model comparison in parameter estimation problems for distributed parameter systems. J Math Bio 1990;28:501–27.CrossRefGoogle Scholar
  2. Berger JO. Statistical decision theory and bayesian analysis, 2nd ed. New York: Springer; 1985.Google Scholar
  3. Bickel P, Doksum K. Mathematical statistics. Oakland: Holden-Day; 1977.Google Scholar
  4. Cressie N. Statistics for spatial data. New York: Wiley; 1991.Google Scholar
  5. Fitzpatrick BG. Bayesian analysis in inverse problems. Inverse Probl 1991;7(5):675–702.CrossRefGoogle Scholar
  6. Gallant AR. Nonlinear statistical models. New York: Wiley; 1987.Google Scholar
  7. Huet S, Bouvier A, Poursat M, Jolivet E. Statistical tools for nonlinear regression, 2nd ed. New York: Springer; 2004.Google Scholar
  8. Wand MP, Jones MC. Kernel smoothing. London: Chapman and Hall; 1995.Google Scholar
  9. Yaglom A. Correlation theory of stationary and related random functions I. New York: Springer; 1987.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsLoyola Marymount UniversityLos AngelesUSA
  2. 2.Tempest TechnologiesLos AngelesUSA

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