American Institute of Mathematical Sciences

Advanced
2008, 5(4): 647-667. doi: 10.3934/mbe.2008.5.647

Quantifying uncertainty in the estimation of probability distributions

H.T. Banks 1, and  Jimena L. Davis 1,

1. 

Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8205, United States

Received  December 2007 Revised  March 2008 Published  October 2008

We consider ordinary least squares parameter estimation problems where the unknown parameters to be estimated are probability distributions. A computational framework for quantification of uncertainty (e.g., standard errors) associated with the estimated parameters is given and sample numerical findings are presented.
Keywords: parameter estimation, asymptotic standard error theory, confidence bands, probability distributions, approximation, size-structured populations.
Mathematics Subject Classification: 35L60,62E20,62F25,62G15,65M32,92D25.
Citation: H.T. Banks, Jimena L. Davis. Quantifying uncertainty in the estimation of probability distributions. Mathematical Biosciences & Engineering, 2008, 5 (4) : 647-667. doi: 10.3934/mbe.2008.5.647
[1]

Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu. Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences & Engineering, 2005, 2 (2) : 289-315. doi: 10.3934/mbe.2005.2.289
[2]

József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249
[3]

Blaise Faugeras, Olivier Maury. An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter estimation procedure: Application to the Indian Ocean skipjack tuna fishery. Mathematical Biosciences & Engineering, 2005, 2 (4) : 719-741. doi: 10.3934/mbe.2005.2.719
[4]

Dongxue Yan, Xianlong Fu. Asymptotic behavior of a hierarchical size-structured population model. Evolution Equations & Control Theory, 2018, 7 (2) : 293-316. doi: 10.3934/eect.2018015
[5]

Qihua Huang, Hao Wang. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness. Mathematical Biosciences & Engineering, 2016, 13 (4) : 697-722. doi: 10.3934/mbe.2016015
[6]

Mustapha Mokhtar-Kharroubi, Quentin Richard. Spectral theory and time asymptotics of size-structured two-phase population models. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 2969-3004. doi: 10.3934/dcdsb.2020048
[7]

József Z. Farkas, Thomas Hagen. Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1825-1839. doi: 10.3934/cpaa.2009.8.1825
[8]

Dongxue Yan, Xianlong Fu. Asymptotic analysis of a spatially and size-structured population model with delayed birth process. Communications on Pure & Applied Analysis, 2016, 15 (2) : 637-655. doi: 10.3934/cpaa.2016.15.637
[9]

Dongxue Yan, Yu Cao, Xianlong Fu. Asymptotic analysis of a size-structured cannibalism population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1975-1998. doi: 10.3934/dcdsb.2016032
[10]

Azmy S. Ackleh, Jeremy J. Thibodeaux. Parameter estimation in a structured erythropoiesis model. Mathematical Biosciences & Engineering, 2008, 5 (4) : 601-616. doi: 10.3934/mbe.2008.5.601
[11]

H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183
[12]

Xianlong Fu, Dongmei Zhu. Stability analysis for a size-structured juvenile-adult population model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 391-417. doi: 10.3934/dcdsb.2014.19.391
[13]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203
[14]

Xianlong Fu, Dongmei Zhu. Stability results for a size-structured population model with delayed birth process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 109-131. doi: 10.3934/dcdsb.2013.18.109
[15]

Jixun Chu, Pierre Magal. Hopf bifurcation for a size-structured model with resting phase. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4891-4921. doi: 10.3934/dcds.2013.33.4891
[16]

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041
[17]

Yunfei Lv, Yongzhen Pei, Rong Yuan. On a non-linear size-structured population model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3111-3133. doi: 10.3934/dcdsb.2020053
[18]

Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233-258. doi: 10.3934/mbe.2015.12.233
[19]

Dan Zhang, Xiaochun Cai, Lin Wang. Complex dynamics in a discrete-time size-structured chemostat model with inhibitory kinetics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3439-3451. doi: 10.3934/dcdsb.2018327
[20]

Georgy P. Karev. Dynamics of heterogeneous populations and communities and evolution of distributions. Conference Publications, 2005, 2005 (Special) : 487-496. doi: 10.3934/proc.2005.2005.487

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences