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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 4: 647-667. doi: 10.3934/mbe.2008.5.647
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Quantifying uncertainty in the estimation of probability distributions

  • 1.
    Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8205
  • Received: 01 December 2007 Accepted: 29 June 2018 Published: 01 October 2008

  • MSC : 35L60,62E20,62F25,62G15,65M32,92D25

  • 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.

    Citation: H.T. Banks, Jimena L. Davis. Quantifying uncertainty in the estimation of probability distributions[J]. Mathematical Biosciences and Engineering, 2008, 5(4): 647-667. doi: 10.3934/mbe.2008.5.647

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  • 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.


  • This article has been cited by:

    1. H. T. Banks, J. E. Banks, S. L. Joyner, Estimation in time-delay modeling of insecticide-induced mortality, 2009, 17, 0928-0219, 10.1515/JIIP.2009.012
    2. H. T. Banks, Jimena L. Davis, Shuhua Hu, 2010, Chapter 2, 978-3-642-11277-5, 19, 10.1007/978-3-642-11278-2_2
    3. H T Banks, Jimena L Davis, Stacey L Ernstberger, Shuhua Hu, Elena Artimovich, Arun K Dhar, Experimental design and estimation of growth rate distributions in size-structured shrimp populations, 2009, 25, 0266-5611, 095003, 10.1088/0266-5611/25/9/095003
    4. H. T. Banks, John E. Banks, Natalie G. Cody, Mark S. Hoddle, Annabel E. Meade, Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period, 2019, 13, 1751-3758, 422, 10.1080/17513758.2019.1616839
    5. Nonlinear stochastic Markov processes and modeling uncertainty in populations, 2012, 9, 1551-0018, 1, 10.3934/mbe.2012.9.1
    6. 2012, 978-1-4398-8083-8, 241, 10.1201/b12209-19
    7. E. M. Rutter, H. T. Banks, K. B. Flores, Estimating intratumoral heterogeneity from spatiotemporal data, 2018, 77, 0303-6812, 1999, 10.1007/s00285-018-1238-6
    8. K. Wendelsdorf, G. Dean, Shuhua Hu, S. Nordone, H.T. Banks, Host immune responses that promote initial HIV spread, 2011, 289, 00225193, 17, 10.1016/j.jtbi.2011.08.012
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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