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.
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References
Banks HT, Fitzpatrick BG. Statistical tests for model comparison in parameter estimation problems for distributed parameter systems. J Math Bio 1990;28:501–27.
Berger JO. Statistical decision theory and bayesian analysis, 2nd ed. New York: Springer; 1985.
Bickel P, Doksum K. Mathematical statistics. Oakland: Holden-Day; 1977.
Cressie N. Statistics for spatial data. New York: Wiley; 1991.
Fitzpatrick BG. Bayesian analysis in inverse problems. Inverse Probl 1991;7(5):675–702.
Gallant AR. Nonlinear statistical models. New York: Wiley; 1987.
Huet S, Bouvier A, Poursat M, Jolivet E. Statistical tools for nonlinear regression, 2nd ed. New York: Springer; 2004.
Wand MP, Jones MC. Kernel smoothing. London: Chapman and Hall; 1995.
Yaglom A. Correlation theory of stationary and related random functions I. New York: Springer; 1987.
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.
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Fitzpatrick, B.G. Statistical Considerations and Techniques for Understanding Physiological Data, Modeling, and Treatments. Cardiovasc Eng 8, 135–143 (2008). https://doi.org/10.1007/s10558-007-9052-6
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DOI: https://doi.org/10.1007/s10558-007-9052-6