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2015 | OriginalPaper | Buchkapitel

6. Fitting Models to Data

verfasst von : Maia Martcheva

Erschienen in: An Introduction to Mathematical Epidemiology

Verlag: Springer US

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Abstract

This chapter is focused on fitting models to data. Least square fit is explained and least square error is defined. Fitting models to data is illustrated on examples and MATLAB code for the fitting is given. This chapter also gives a point-by-point list of steps that should be followed when fitting is performed. The concepts of model selection and the Akaike Information Criterion are introduced and illustrated on examples. Computing elasticities and sensitivities is explained.

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Literatur
4.
Zurück zum Zitat H. Akaike, Information theory and an extension of the maximum likelihood principle, in Second International Symposium on Information Theory (Tsahkadsor, 1971), Akadémiai Kiadó, Budapest, 1973, pp. 267–281. H. Akaike, Information theory and an extension of the maximum likelihood principle, in Second International Symposium on Information Theory (Tsahkadsor, 1971), Akadémiai Kiadó, Budapest, 1973, pp. 267–281.
31.
Zurück zum Zitat K. P. Burnham and D. R. Anderson, Model selection and multimodel inference: A practical information-theoretic approach, Springer, New York, second ed., 2002. K. P. Burnham and D. R. Anderson, Model selection and multimodel inference: A practical information-theoretic approach, Springer, New York, second ed., 2002.
32.
Zurück zum Zitat K. P. Burnham and D. R. Anderson, Multimodel inference: understanding AIC and BIC in model selection, Sociol. Methods Res., 33 (2004), pp. 261–304.MathSciNetCrossRef K. P. Burnham and D. R. Anderson, Multimodel inference: understanding AIC and BIC in model selection, Sociol. Methods Res., 33 (2004), pp. 261–304.MathSciNetCrossRef
53.
Zurück zum Zitat R. P. Dickinson and R. J. Gelinas, Sensitivity analysis of ordinary differential equation systems—a direct method, J. Computational Phys., 21 (1976), pp. 123–143.MathSciNetCrossRefMATH R. P. Dickinson and R. J. Gelinas, Sensitivity analysis of ordinary differential equation systems—a direct method, J. Computational Phys., 21 (1976), pp. 123–143.MathSciNetCrossRefMATH
68.
Zurück zum Zitat J. W. Haefner, Modeling biological systems: principles and applications, Springer, New York, second ed., 2005. With 1 CD-ROM (Windows and UNIX). J. W. Haefner, Modeling biological systems: principles and applications, Springer, New York, second ed., 2005. With 1 CD-ROM (Windows and UNIX).
77.
Zurück zum Zitat C. M. Hurvich and C.-L. Tsai, Regression and time series model selection in small samples, Biometrika, 76 (1989), pp. 297–307.MathSciNetCrossRefMATH C. M. Hurvich and C.-L. Tsai, Regression and time series model selection in small samples, Biometrika, 76 (1989), pp. 297–307.MathSciNetCrossRefMATH
79.
Zurück zum Zitat V. Isham, Stochastic models of epidemics with special reference to AIDS, The Annals of Applied Probability, 3 (1993), pp. 1–27.MathSciNetCrossRefMATH V. Isham, Stochastic models of epidemics with special reference to AIDS, The Annals of Applied Probability, 3 (1993), pp. 1–27.MathSciNetCrossRefMATH
106.
Zurück zum Zitat M. Martcheva, India’s approach to eliminating plasmodium falciparum malaria: A modeling perspective, J. Biol. Systems, 18 (2010), pp. 867–891.MathSciNetCrossRef M. Martcheva, India’s approach to eliminating plasmodium falciparum malaria: A modeling perspective, J. Biol. Systems, 18 (2010), pp. 867–891.MathSciNetCrossRef
119.
Zurück zum Zitat H. Motulsky and A. Christopoulos, Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting, GraphPad Software Inc., San Diego, 2003. H. Motulsky and A. Christopoulos, Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting, GraphPad Software Inc., San Diego, 2003.
122.
Zurück zum Zitat U. Nations, The Millemnnium Development Goals Report 2010, United Nations, New York, 2010. U. Nations, The Millemnnium Development Goals Report 2010, United Nations, New York, 2010.
129.
Zurück zum Zitat F. Nyabadza, A mathematical model for combating HIV/AIDS in Southern Africa: Will multiple strategies work?, J. Biol. Sys., 14 (2006), pp. 357–372.MathSciNetCrossRefMATH F. Nyabadza, A mathematical model for combating HIV/AIDS in Southern Africa: Will multiple strategies work?, J. Biol. Sys., 14 (2006), pp. 357–372.MathSciNetCrossRefMATH
133.
Zurück zum Zitat T. L. Paez, Introduction to model validation, in Proceedings of the IMAC-XXVII, Society for Experimental Mechanics, US, 2009, pp. 1–11. T. L. Paez, Introduction to model validation, in Proceedings of the IMAC-XXVII, Society for Experimental Mechanics, US, 2009, pp. 1–11.
139.
Zurück zum Zitat H. J. Rose, The use of amantadine and influenza vaccine in a type a influenza epidemic in a boarding school, Journal of Royal College of General Practitioners, 30 (1980), pp. 619–621. H. J. Rose, The use of amantadine and influenza vaccine in a type a influenza epidemic in a boarding school, Journal of Royal College of General Practitioners, 30 (1980), pp. 619–621.
Metadaten
Titel
Fitting Models to Data
verfasst von
Maia Martcheva
Copyright-Jahr
2015
Verlag
Springer US
DOI
https://doi.org/10.1007/978-1-4899-7612-3_6

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