Canonical Modeling: A Link Between Environmental Models and Statistics
DOI:
https://doi.org/10.17713/ajs.v27i1&2.534Abstract
The article describes three connections between statistics and modeling in environmental studies. As the first connection, typical exposure and disease models are derived mathematically from general principles of dynamical systems analysis. The second connection is developed between physiological and environmental processes on one hand and survival curves on the other. The third connection describes how dynamic processes affect distributions of random variables. Forming novel connections between different branches of environmetrics enhances our understanding of environmental phenomena and offers new avenues of analysis.References
D.R. Cox. Regression models and life tables (with discussion). J. R. Stat. Soc. B. 34: 187-220, 1972.
A.E.N. Ferreira. Linked lists representation of S-systems: An alternative way to implement numerical algorithms (Abstract). Second S-System Symposium, Tampa, FL, 1992.
E.D. Ford. Competition and stand structure in some even-aged plant monocultures. J. Ecology 63: 311-333, 1975.
D.J. Gates, R. McMurtrie, and C.J. Borough. Skewness reversal of distribution of stem diameter in plantations of Pinus radiata. Australian For. Res. 13: 267-270, 1983.
W.H. Hallenbeck. Quantitative Risk Assessment for Environmental and Occupational Health. Lewis Publ., Boca Raton, 1993.
D.H. Irvine and M.A. Savageau. Efficient solution of nonlinear ordinary differential equations expressed in S-system canonical form. SIAM J. Numer. Anal. 27: 704-735, 1990.
C.L. Mohler, P.L. Marks, and D.G. Sprugel. Stand structure and allometry of trees during self-thinning of pure stands. J. Ecology 66: 599-614, 1978.
A.M. Mood, F.A. Graybill, and D.C. Boes. Introduction to the Theory of Statistics (3rd ed.), McGraw-Hill, New York, 1983.
P.B. Ryan. An overview of human exposure modeling, J. Exp. Anal. Envir. Epidem. 1(4): 453-474, 1991.
K.J. Rothman. Modern Epidemiology. Little, Brown and Company, Boston, 1986.
M.A. Savageau. Biochemical systems analysis, I. Some mathematical properties of the rate law for the component enzymatic reactions. J. Theor. Biol. 25: 365-369, 1969a.
M.A. Savageau. Biochemical systems analysis, II. The steady-state solutions for an npool system using a power-law approximation. J. Theor. Biol. 25: 370-379, 1969b.
M.A. Savageau. The behavior of intact biochemical control systems. Curr. Top. Cell Reg. 6: 63-130, 1972.
M.A. Savageau. Optimal design of feedback control by inhibition: Steady-state considerations. J. Mol. Evol. 4: 139-156, 1974.
M.A. Savageau. Biochemical Systems Analysis. A Study of Function and Design in Molecular Biology. Addison-Wesley, Reading, Massachusetts, 1976.
M.A. Savageau. Growth of complex systems can be related to the properties of their underlying determinants. Proc. Nat. Acad. Sci. 76: 5413-5417, 1979a.
M.A. Savageau. Allometric morphogenesis of complex systems: Derivation of the basic equations from first principles. Proc. Nat. Acad. Sci. USA. 76: 6023-6025, 1979b.
M.A. Savageau. Growth equations: A general equation and a survey of special cases. Math. Biosci. 48: 267-278, 1980.
M.A. Savageau. A suprasystem of probability distributions. Biometr. J. 24: 323-330, 1982.
M.A. Savageau and E.O. Voit. Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Math. Biosci. 87: 83-115, 1987.
N.V. Torres, E.O. Voit, and C. H. Alcón. Optimization of nonlinear biotechnological processes with linear programming. Application to citric acid production in Aspergillus niger. Biotechn. Bioengin. 49: 247-258, 1996.
N.V. Torres, E.O. Voit, C. Glez-Alcón, and F. Rodríguez. An integrated optimization method for biochemical systems. Description of method and application to ethanol, glycerol and carbohydrate production in Saccharomyces cerevisiae, Biotechn.
Bioengin. 55(5): 758-772, 1997.
E.O. Voit, editor. Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity. Van Nostrand Reinhold, New York, 1991.
E.O. Voit. Optimization in integrated biochemical systems. Biotechn. Bioengin. 40: 572-582, 1992a.
E.O. Voit. The S-distribution. A tool for approximation and classification of univariate, unimodal probability distributions. Biometr. J. 34: 855-878, 1992b.
E.O. Voit. S-system modelling of complex systems with chaotic input. Environmetrics 4: 153-186, 1993.
E.O. Voit, W. L. Balthis, and R. A. Holser. Hierarchical Monte Carlo modeling with Sdistributions: Concepts and illustrative analysis of mercury contamination in king mackerel. Environment International 21: 627-635, 1995.
E.O. Voit, D.H. Irvine, and M.A. Savageau. The User's Guide to ESSYNS. Medical University of South Carolina Press, Charleston, 1989.
E.O. Voit and R.G. Knapp. Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description, Statistics in Medicine 16: 1705-1729, 1997.
E.O. Voit and P.F. Rust. Tutorial: S-system analysis of continuous univariate probability distributions. J. Statist. Comput. Simul. 42: 187-249, 1992.
E.O. Voit and M.K. Schubauer-Berigan. The role of canonical modeling as a unifying framework for ecological and human risk assessment. In M.C. Newman and C. Strojan, editors, Risk Assessment: Logic and Measurement. Ann Arbor Press, Chelsea, MI, 1998.
E.O. Voit and A. Sorribas. Computer modeling of dynamically changing distributions of random variables, Mathematical and Computer Modelling, in press, 1998.
E.O. Voit, and S. Yu. The S-distribution. Approximation of discrete distributions. Biometr. J. 36: 205-219, 1994.
S. Yu and E.O. Voit. A simple, flexible failure model. Biometrical J. 37: 595-609, 1995.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
