A comparison of approximation methods for the estimation of probability distributions on parameters

Applied Numerical Mathematics

Volumn 57, Issue 5-7 SPEC. ISS., 2007, Pages 753-777

  Banks, H T ^a   Davis, Jimena L ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; SENSITIVITY ANALYSIS;

DELTA FUNCTION; GROWTH RATE DISTRIBUTIONS; MOSQUITOFISH POPULATIONS; SIZE-STRUCTURED POPULATION;

APPROXIMATION THEORY;

EID: 34147185357     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.07.016     Document Type: Article

References (36)

1. Banks H.T. Remarks on uncertainty assessment and management in modeling and computation. Math. Comput. Modelling 33 (2001) 39-47
2. Banks H.T., and Bihari K.L. Modelling and estimating uncertainty in parameter estimation. Inverse Problems 17 (2001) 95-111
3. Banks H.T., Bortz D.M., Pinter G.A., and Potter L.K. Modeling and imaging techniques with potential for application in bioterrorism. CRSC-TR03-02, January, 2003. In: Banks H.T., and Castillo-Chavez C. (Eds). Bioterrorism: Mathematical Modeling Applications in Homeland Security. Frontiers in Applied Math. vol. FR28 (2003), SIAM, Philadelphia, PA 129-154 (Chapter 6)
4. Banks H.T., Botsford L.W., Kappel F., and Wang C. Modeling and estimation in size structured population models. LCDS-CCS Report 87-13, Brown University. Proceedings 2nd Course on Mathematical Ecology. Trieste, 8-12 December, 1986 (1988), World Press, Singapore 521-541
5. Banks H.T., and Gibson N.L. Well-posedness in Maxwell systems with distributions of polarization relaxation parameters. CRSC-TR04-01, NCSU, January, 2004. Appl. Math. Lett. 18 (2005) 423-430
6. H.T. Banks, N.L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters, CRSC-TR05-29, August, 2005, Quarterly Appl. Math., in press
7. H.T. Banks, D.W. Iles, A comparison of stability and convergence properties of techniques for inverse problems, LCDS 86-3, Brown University, Providence, RI, January 1986
8. Banks H.T., and Iles D.W. On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems. In: Lasiecka I., and Triggiani R. (Eds). Control Problems for Systems Described by Partial Differential Equations and Applications. Lecture Notes in Control and Inf. Sci. vol. 97 (1987), Springer-Verlag, Berlin 130-142
9. Banks H.T., and Fitzpatrick B.G. Estimation of growth rate distributions in size-structured population models. CAMS Tech. Rep. 90-2, University of Southern California, January 1990. Quart. Appl. Math. 49 (1991) 215-235
10. Banks H.T., Fitzpatrick B.G., Potter L.K., and Zhang Y. Estimation of probability distributions for individual parameters using aggregate population data, CRSC-TR98-6, January 1998. In: McEneaney W., Yin G., and Zhang Q. (Eds). Stochastic Analysis, Control, Optimization and Applications (1998), Birkhäuser, Basel 353-371
11. Banks H.T., and Kunisch K. Estimation Techniques for Distributed Parameter Systems (1989), Birkhäuser, Boston
12. Banks H.T., and Pinter G.A. A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue. CRSC-TR04-03, N.C. State University, January 2004. SIAM J. Multiscale Modeling Simulation 3 (2005) 395-412
13. Banks H.T., and Potter L.K. Probabilistic methods for addressing uncertainty and variability in biological models: Application to a toxicokinetic model. CRSC-TR02-27, N.C. State University, September 2002. Math. Biosci. 192 (2004) 193-225
14. Beal S.L., and Sheiner L.B. Estimating population kinetics. CRC Critical Rev. Biomed. Engrg. 8 (1982) 195-222
15. Billingsley P. Convergence of Probability Measures (1968), Wiley, New York
16. Burden R.L., and Douglas Faires J. Numerical Analysis. third ed. (1985), PWS Publishers, Boston
17. Davidian M., and Gallant A.R. Smooth nonparametic maximum likelihood estimation for population pharmacokinetrics, with application to quinidine. J. Pharm. Biopharm. 20 (1992) 529-556
18. Davidian M., and Gallant A.R. The nonlinear mixed effects model with a smooth random effects density. Biometrika 80 (1993) 475-488
19. Davidian M., and Gilitan D.M. Nonlinear Models for Repeated Measurement Data (1995), Chapman & Hall, London
20. Davidian M., and Gilitan D.M. Nonlinear models for repeated measurement data: An overview and update. J. Agricultural, Biol. Environ. Statist. 8 (2003) 387-419
21. M.V. Evans, W.K. Boyes, P.J. Bushnell, J.H. Raymer, J.E. Simmons, A physiologically based pharmacokinetic modle for trichloroethylene (TCE) in Long-Evans rats, preprint, 1999
22. Gallant A.R. Nonlinear Statistical Models (1987), Wiley, New York
23. N.L. Gibson, Terahertz-based electromagnetic interrogation techniques for damage detection, PhD thesis, N.C. State University, Raleigh, August 2004
24. Hogg R.V., and Tanis E.A. Probability and Statistical Inference (2001), Prentice Hall, Upper Saddle River
25. Jennrich R.I. Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40 (1969) 633-643
26. Lindsay B.G. The geometry of mixture likelihoods: A general theory. Ann. Statist. 11 (1983) 86-94
27. Lindsay B.G. Mixture Models: Theory, Geometry and Applications. NSF-CBMS Regional Conf. Series in Probability and Statistics vol. 5 (1995), Institute Mathematical Statistics, Haywood, CA
28. Lindsay B.G., and Lesperance M.L. A review of semiparametric mixture models. J. Statist. Plannning Inference 47 (1995) 29-39
29. Mallet A. A maximum likelihood estimation method for random coefficient regression models. Biometrika 73 (1986) 645-656
30. Sheiner L.B., Rosenberg B., and Melmon K. Modeling of individual pharmacokinetics for computer-aided drug dosage. Comp. Biomed. Res. 5 (1972) 441-459
31. L.K. Potter, Physiologically based pharmacokinetic models for the systemic transport of trichloroethylene, PhD thesis, N.C. State University, August, 2001, http://www.lib.ncsu.edu
32. Quarteroni A., Sacco R., and Saleri F. Numerical Mathematics (2000), Springer, New York
33. Schumitzky A. Nonparametric EM algorithms for estimating prior distributions. Appl. Math. Comput. 45 (1991) 141-157
34. Schumitzky A. The nonparametric maximum likelihood approach to pharmacokinetic population analysis. Proceedings of the Western Simulation Multiconference-Simulation in Health Care (1993), Society for Computer Simulation, San Diego, CA
35. Wahba G. Bayesian "confidence intervals" for the cross-validated smoothing spline. J. Roy. Statist. Soc. B 45 (1983) 133-150
36. Wahba G. (Smoothing) splines in nonparametric regression. In: El-Shaarawi A., and Piegorsch W. (Eds). Dept. of Statistics-TR 1024, Univ. Wisconsin, September, 2000. Encyclopedia of Environmetrics vol. 4 (2001), Wiley, New York 2099-2112