IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v32y1990i5p553-560.html
   My bibliography  Save this article

Characterization of non-connected parameter uncertainty regions

Author

Listed:
  • Piet-Lahanier, H.
  • Walter, E.

Abstract

Set-membership estimation (or parameter bounding) uses a non-statistical description of the acceptable error between the measurements and corresponding model outputs in the form of prior upper and lower bounds. It aims at characterizing the set S of all parameter vectors that are consistent with the data when these bounds are taken into account. It does not rely on any asymptotic theory, which makes it particularly suitable for applications where the number of data points is very limited, such as is often the case in biology for example. In this paper, we describe an improved version of an algorithm recently proposed for determining the feasible parameter set (or membership set) associated with models whose outputs are nonlinear in their parameters. The method now allows the description of non-connected sets. It is applied to simulated examples that illustrate some practical problems where S turns out not to be connected.

Suggested Citation

  • Piet-Lahanier, H. & Walter, E., 1990. "Characterization of non-connected parameter uncertainty regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 553-560.
    • Handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:553-560
    DOI: 10.1016/0378-4754(90)90011-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475490900117
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(90)90011-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Walter, E. & Piet-Lahanier, H. & Happel, J., 1986. "Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(6), pages 479-490.
    3. Pronzato, Luc & Walter, Eric & Venot, Alain & Lebruchec, Jean-Francois, 1984. "A general-purpose global optimizer: Implimentation and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(5), pages 412-422.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Pronzato, Luc & Walter, Eric, 1990. "Experiment design for bounded-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 571-584.
    3. Keesman, Karel, 1990. "Membership-set estimation using random scanning and principal component analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 535-543.
    4. Marco Stenborg Petterson & David Seim & Jesse M. Shapiro, 2023. "Bounds on a Slope from Size Restrictions on Economic Shocks," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 552-572, August.
    5. Shary, Sergey P., 1995. "Solving the linear interval tolerance problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 53-85.
    6. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
    7. Enríquez, R. & Jiménez, M.J. & Heras, M.R., 2017. "Towards non-intrusive thermal load Monitoring of buildings: BES calibration," Applied Energy, Elsevier, vol. 191(C), pages 44-54.
    8. Kumar, Rajeeva & Kabamba, Pierre T. & Hyland, David C., 2005. "Analysis and parameter selection for an adaptive random search algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 95-103.
    9. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
    10. Walter, E. & Piet-Lahanier, H. & Happel, J., 1986. "Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(6), pages 479-490.
    11. da Silva, Ivan N. & de Arruda, Lucia V.R. & do Amaral, Wagner C., 1999. "A novel approach to robust parameter estimation using neurofuzzy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 251-268.
    12. Piet-Lahanier, Hélène & Veres, Sándor M. & Walter, Eric, 1992. "Comparison of methods for solving sets of linear inequalities in the bounded-error context," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(6), pages 515-524.
    13. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:553-560. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.