An inverse problem statistical methodology summary

Mathematical and Statistical Estimation Approaches in Epidemiology

Volumn , Issue , 2009, Pages 249-302

  Banks, H Thomas ^a   Davidian, Marie ^a   Samuels Jr , John R ^a   Sutton, Karyn L ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Inference; Least squares inverse problems; Parameter estimation; Sensitivity and generalized sensitivity functions

Indexed keywords

EID: 77955412236     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-90-481-2313-1_11     Document Type: Chapter

References (36)

1. Banks HT, Banks JE, Dick LK, Stark JD (2007) Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides, CRSC-TR05-22, May, 2005. Bull. Math. Biol. 69:2139-2180.
2. Banks HT, Dediu S, Ernstberger SE (2007) Sensitivity functions and their uses in inverse problems, CRSC-TR07-12, July, 2007. J. Inv. Ill-Posed Probl. 15:683-708.
3. Banks HT, Dediu S, Nguyen HK (2007) Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space, CRSC-TR06-25, September, 2006. Math. Biosci. Eng. 4:403-430.
4. Banks HT, Ernstberger SL, Grove SL (2006) Standard errors and confidence intervals in inverse problems: Sensitivity and associated pitfalls, CRSC-TR06-10, March, 2006. J. Inv. Ill-Posed Probl. 15:1-18.
5. Banks HT, Fitzpatrick BG (1989) Inverse problems for distributed systems: Statistical tests and ANOVA, LCDS/CCS Rep. 88-16, July, 1988, Brown University; Proc. International Symposium on Math. Approaches Envir. Ecol. Probl. Springer Lecture Note Biomath. 81:262-273.
6. Banks HT, Fitzpatrick BG (1990) Statistical methods for model comparison in parameter estimation problems for distributed systems, CAMS Tech. Rep. 89-4, September, 1989, University of Southern California. J. Math. Biol. 28:501-527.
7. Banks HT, Kareiva P (1983) Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models, LCDS Report #82-13, July 1982, Brown University; J. Math. Biol. 17:253-273.
8. Banks HT, Kunsich K (1989) Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston.
9. Banks HT, Nguyen HK (2006) Sensitivity of dynamical system to Banach space parameters, CRSC-TR05-13, February, 2005. J. Math. Anal. Appl. 323:146-161.
10. Bai P, Banks HT, Dediu S, Govan AY, Last M, Loyd A, Nguyen HK, Olufsen MS, Rempala G, Slenning BD (2007) Stochastic and deterministic models for agricultural production networks, CRSC-TR07-06, February, 2007. Math. Biosci. and Engineering 4:373-402.
11. Batzel JJ, Kappel F, Schneditz D, Tran HT (2006) Cardiovascular and Respiratory Systems: Modeling, Analysis and Control. SIAM, Philadelphia.
12. Baumeister J (1987) Stable Solution of Inverse Problems. Vieweg, Braunschweig.
13. Bedrick EJ, Tsai CL (1994) Model selection for multivariate regression in small samples. Biometrics 50:226-231.
14. Bozdogan H (1987) Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika 52:345-370.
15. Bozdogan H (2000) Akaike's Information Criterion and recent developments in information complexity. J. Math. Psychol. 44:62-91.
16. Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer, Berlin Heidelberg New York.
17. Burnham KP, Anderson DR (2004) Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods and Research 33:261-304.
18. Carroll RJ, Ruppert D (1988) Transformation andWeighting in Regression. Chapman & Hall, New York.
19. Casella G, Berger RL (2002) Statistical Inference. Duxbury, California.
20. Chalmond B (2003) Modeling and Inverse Problems in Image Analysis. Springer, Berlin Heidelberg New York.
21. Cruz JB (ed) (1973) System Sensitivity Analysis. Dowden, Hutchinson & Ross, Stroudsberg, PA.
22. Davidian M, Giltinan D (1998) Nonlinear Models for Repeated Measurement Data. Chapman & Hall, London.
23. Engl HW, Hanke M, Neubauer A (1996) Regularization of Inverse Problems. Kluwer, Dordrecht.
24. Eslami M(1994) Theory of Sensitivity in Dynamic Systems: An Introduction. Springer, Berlin Heidelberg New York.
25. Frank PM (1978) Introduction to System Sensitivity Theory. Academic, New York.
26. Gallant AR (1987) Nonlinear Statistical Models. Wiley, New York.
27. Gelb A (ed) (1979) Applied Optimal Estimation. MIT Press, Cambridge.
28. Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76: 297-307.
29. Jennrich RI (1969) Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40:633-643.
30. Saltelli A, Chan K, Scott EM (eds) (2000) Sensitivity Analysis. Wiley, New York.
31. Seber GAF, Wild CJ (1989) Nonlinear Regression. Wiley, New York.
32. Sutton KL, Banks HT, Castillo-Chávez C (2008) Estimation of invasive pneumococcal disease dynamic parameters and the impact of conjugate vaccination in Australia, CRSC-TR07-15, August, 2007. Math. Biosci. Eng. 5:175-204.
33. Tarantola A (2004) Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM, Philadelphia.
34. Thomaseth K, Cobelli C (1999) Generalized sensitivity functions in physiological system identification. Ann. Biomed. Eng. 27(5):607-616.
35. Vogel CR (2002) Computational Methods for Inverse Problems. SIAM, Philadelphia.
36. Wackerly DD, Mendenhall III W, Scheaffer RL (2002) Mathematical Statistics with Applications. Duxbury Thompson Learning, USA.