Parameter estimation in a coupled system of nonlinear size-structured populations.

A least squares technique is developed for identifying unknown parameters in a coupled system of nonlinear size-structured populations. Convergence results for the parameter estimation technique are established. Ample numerical simulations and statistical evidence are provided to demonstrate the feasibility of this approach.

[1]  Jordi Ripoll,et al.  Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status. , 2004, Mathematical biosciences.

[2]  Determining a coefficient in a first-order hyperbolic equation , 1991 .

[3]  A. Mallet.  A maximum likelihood estimation method for random coefficient regression models , 1986 .

[4]  Odo Diekmann,et al.  THE "CUMULATIVE" FORMULATION OF (PHYSIOLOGICALLY) STRUCTURED POPULATION MODELS , 1992 .

[5]  Douglas W. Nychka,et al.  The Average Posterior Variance of a Smoothing Spline and a Consistent Estimate of the Average Squared Error , 1990 .

[6]  Harvey Thomas Banks,et al.  Nonlinear Reptation in Molecular Based Hysteresis Models for Polymers , 2004 .

[7]  Harvey Thomas Banks,et al.  Modeling and Imaging Techniques with Potential for Application in Bioterrorism , 2003 .

[8]  Harvey Thomas Banks,et al.  Estimation of growth rate distributions in size structured population models , 1991 .

[9]  Douglas Nychka,et al.  Bayesian Confidence Intervals for Smoothing Splines , 1988 .

[10]  J E Banks,et al.  Population dynamics models in plant-insect herbivore-pesticide interactions. , 2005, Mathematical biosciences.

[11]  Muni S. Srivastava,et al.  Regression Analysis: Theory, Methods, and Applications , 1991 .

[12]  G. Wahba.  Bayesian "Confidence Intervals" for the Cross-validated Smoothing Spline , 1983 .

[13]  Marie Davidian,et al.  The Nonlinear Mixed Effects Model with a Smooth Random Effects Density , 1993 .

[14]  D M Bortz,et al.  Incorporation of variability into the modeling of viral delays in HIV infection dynamics. , 2003, Mathematical biosciences.

[15]  William Rundell,et al.  A Regularization Scheme for an Inverse Problem in Age-Structured Populations , 1994 .

[16]  Harvey Thomas Banks,et al.  Multiscale Considerations in Modeling of Nonlinear Elastomers , 2007 .

[17]  Waltraud Huyer.  A Size-Structured Population-Model with Dispersion , 1994 .

[18]  O. Diekmann,et al.  The Dynamics of Physiologically Structured Populations , 1986 .

[19]  Marie Davidian,et al.  Nonlinear models for repeated measurement data: An overview and update , 2003 .

[20]  D. M. Titterington,et al.  On confidence bands in nonparametric density estimation and regression , 1988 .

[21]  Harvey Thomas Banks,et al.  Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis) , 1991 .

[22]  H. T. Banks,et al.  A Probabilistic Multiscale Approach to Hysteresis in Shear Wave Propagation in Biotissue , 2005, Multiscale Model. Simul..

[23]  A. V. D. Vaart,et al.  Efficient maximum likelihood estimation in semiparametric mixture models , 1996 .

[24]  Chung-Ki Cho,et al.  Parameter Estimation for Age-Structured Population Dynamics , 1997 .

[25]  H. T. Banks,et al.  Well-posedness in Maxwell systems with distributions of polarization relaxation parameters , 2005, Appl. Math. Lett..

[26]  Ming Jiang,et al.  Bioterrorism. Mathematical modeling applications in homeland security. , 2005 .

[27]  William Rundell.  Determining the Death Rate for an Age-Structured Population from Census Data , 1993, SIAM J. Appl. Math..

[28]  F A Milner,et al.  Rapidly converging numerical algorithms for models of population dynamics , 1992, Journal of mathematical biology.

[29]  Gabriel Dimitriu.  Parameter Estimation in Size/Age Structured Population Models Using the Moving Finite Element Method , 2002, Numerical Methods and Application.

[30]  M. Grasselli.  An inverse problem in population dynamics , 1997 .

[31]  W. Rundell.  Determining the birth function for an age structured population. , 1989, Mathematical population studies.

[32]  Marie Davidian,et al.  Nonlinear Models for Repeated Measurement Data , 1995 .

[33]  H. Banks,et al.  A finite difference approximation for a coupled system of nonlinear size-structured populations , 2002 .

[34]  Azmy S. Ackleh,et al.  Parameter identification in size-structured population models with nonlinear individual rates , 1999 .

[35]  Harvey Thomas Banks,et al.  Estimation of probability distributions for individual parameters using aggregate population observations , 1999 .

[36]  B. G. Fitzpatrick.  Modeling and estimation problems for structured heterogeneous populations , 1993 .

[37]  Mats Gyllenberg,et al.  The inverse problem of linear age-structured population dynamics , 2002 .

[38]  S. Wood,et al.  Estimation of Mortality Rates in Stage-Structured Population , 1991 .

[39]  Wolfgang Karl Härdle,et al.  Asymptotic maximal deviation of M-smoothers , 1989 .

[40]  Ben G. Fitzpatrick,et al.  Statistical tests of fit in estimation problems for structured population modeling , 1995 .

[41]  B. Lindsay.  The Geometry of Mixture Likelihoods, Part II: The Exponential Family , 1983 .

[42]  A. S. Ackleh.  Parameter estimation in a structured algal coagulation-fragmentation model , 1997 .