Citation: Celia Schacht, Annabel Meade, H.T. Banks, Heiko Enderling, Daniel Abate-Daga. Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7299-7326. doi: 10.3934/mbe.2019365
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[2] | H. T. Banks, S. Hu and W. C. Thompson, Chapter 5 of Modeling and Inverse Problems in the Presence of Uncertainty, Chapman and Hall/CRC, New York, 2014. |
[3] | H. T. Banks, L. W.Botsford, F. Kappel, et al., Modeling and estimation in size structured popu-lation models, LCDS/CCS Rep. 87-13, March, 1987, Brown Univ.; Proc. 2nd Course on Math. Ecology (Trieste, December, 1986), World Scientific Press, Singapore (1988), 521–541. |
[4] | H. T. Banks and H. T. Tran, Chapter 9.7 of Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, Boca Raton, FL, January 2, 2009 |
[5] | H. T. Banks, J. L. Davis, S. L. Ernstberger, et al., Experimental design and estimation of growth rate distributions in size-structured shrimp populations, CRSC TR08-20, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, November, 2008; Inverse Probl., 25 (2009), 095003 (28 pp). |
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[7] | H. T. Banks and B. G. Fitzpatrick, Estimation of growth rate distributions in size-structured popu-lation models, CAMS Tech. Rep. 90-2, University of Southern California, January, 1990; Q. Appl. Math., 49 (1991), 215–235. |
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[11] | H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of di-electric mechanisms and parameters, CRSC-TR05-29, August, 2005; Q. Appl. Math., 64 (2006), 749–795. |
[12] | H. T. Banks and D. M. Bortz, Inverse problems for a class of measure dependent dynamical systems, J. Inverse Ill-pose. Probl., 13 (2005), 103–121. |
[13] | H. T. Banks, D. M. Bortz and S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Math. Biosci., 183 (2003), 63–91. |
[14] | H. T. Banks, D. M. Bortz, G. A. Pinter, et al., Modeling and imaging techniques with potential for application in bioterrorism, CRSC TR03-02, January 2003; Chapter 6 in Bioterrorism: Math-ematical Modeling Applications in Homeland Security (H.T. Banks and C. Castillo-Chavez, eds.), Front. Appl. Math., FR28, SIAM, Philadelphia, 2003, 129–154. |
[15] | H. T. Banks, J. H. Barnes, A. Eberhardt, et al., Modeling and computation of propagating waves from coronary stenosis, Comput. Appl. Math., 21 (2002), 767–788. |
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[18] | H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, CRSC-TR04-03, January, 2004; SIAM J. Multiscale Model. Sim., 3 (2005), 395–412. |
[19] | H. T. Banks, Chapter 14.4 of A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering, Taylor and Frances Publishing, 2012. |
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[26] | H. T. Banks, K. Bekele-Maxwell, R. A. Everett, et al., Dynamic modeling of problem drinkers undergoing behavioral treatment, CRSC-TR16-12, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, October, 2016; Bull. Math. Biol., 79 (2017), 1254–1273. |
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[28] | H. T. Banks, K. B. Flores, I. G. Rosen, et al., The Prohorov Metric Framework and aggregate data inverse problems for random PDEs, CRSC-TR18-05, Center for Research in Scientific Computa- tion, N. C. State University, Raleigh, NC, June, 2018; Commun. Appl. Anal., 22 (2018), 415–446. |
[29] | H. T. Banks, J. Catenacci and S. Hu, Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems, CRSC-TR15-05, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, May, 2015. J. Inverse Ill-pose. P., 24 (2016), 413-–433. |
[30] | H. T. Banks, J. E. Banks, N. G. Cody, et al., Population model for the decline of Homalodisca vitripennis (HEMIPTERA: CICADELLIDAE) over a ten-year period, CRSC-TR18-06, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, June, 2018; J. Biol. Dyn., 13 (2019), 422–446. |
[31] | H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhas-ser, Boston, 1989. |
[32] | H. T. Banks and P. Kareiva, Parameter estimation techniques for transport equations with applica-tion to population dispersal and tissue bulk flow models, J. Math. Biol., 17 (1983), 253–273. |
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[40] | D. Ucinski and A. C. Atkinson, Experimental design for time-dependent models with correlated observations, Stud. Nonlinear Dyn. E., 8 (2004), Article 13: The Berkeley Electronic Press. |
[41] | H. T. Banks, K. Holm and F. Kappel, Comparison of optimal design methods in inverse problems, CRSC-TR10-11, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, July, 2010; Inverse Probl., 27 (2011), 075002. |
[42] | H. T. Banks, A. Cintr'on-Arias and F. Kappel, Parameter selection methods in inverse problem for-mulation, CRSC-TR10-03, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, revised November 2010; Mathematical Model Development and Validation in Physi-ology: Application to the Cardiovascular and Respiratory Systems, Lecture Notes in Mathematics, Vol. 2064, Mathematical Biosciences Subseries; Springer-Verlag, Berlin, 2013. |
[43] | M. Avery, H. T. Banks, K. Basu, et al., Experimental design and inverse problems in plant bi-ological modeling, CRSC-TR11-12, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2011; J. Inverse Ill-pose. P., 20 (2012), 169–191. |
[44] | H. T. Banks and K. L. Rehm, Experimental design for vector output systems, CRSC-TR12-11, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, April, 2012; Inverse Probl. Sci. En., 22 (2014), 557–590. |
[45] | H. T. Banks and K. L. Rehm, Experimental design for distributed parameter vector systems, CRSC-TR12-17, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, August, 2012; Appl. Math. Lett., 26 (2013), 10–14. |
[46] | H. T. Banks, S. Dediu, S. L. Ernstberger, et al., Generalized sensitivities and optimal experimental design, CRSC-TR08-12, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, September, 2008, revised November, 2009; J. Inverse Ill-pose. P., 18 (2010), 25–83. |
[47] | B. M. Adams, H. T. Banks, M. Davidian, et al., Model fitting and prediction with HIV treatment interruption data, CRSC TR05-40, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2005; Bull. Math. Biol., 69 (2007), 563–584. |