IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v21y2016i4d10.1007_s13253-016-0259-0.html
   My bibliography  Save this article

Optimal Design of Dilution Experiments Under Volume Constraints

Author

Listed:
  • Maryam Zolghadr

    (University of Turin)

  • Sergei Zuyev

    (Chalmers University of Technology and University of Gothenburg)

Abstract

The paper develops methods to construct a one-stage optimal design of dilution experiments under the total available volume constraint typical for biomedical applications. We consider various design criteria based on the Fisher information both in Bayesian and non-Bayesian settings and show that the optimal design is typically one-atomic meaning that all the dilutions should be of the same size. The main tool is variational analysis of functions of a measure and the corresponding steepest descent-type numerical methods. Our approach is generic in the sense that it allows for inclusion of additional constraints and cost components, like the cost of materials and of the experiment itself.

Suggested Citation

  • Maryam Zolghadr & Sergei Zuyev, 2016. "Optimal Design of Dilution Experiments Under Volume Constraints," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 663-683, December.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:4:d:10.1007_s13253-016-0259-0
    DOI: 10.1007/s13253-016-0259-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-016-0259-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-016-0259-0?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. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    2. repec:dau:papers:123456789/1906 is not listed on IDEAS
    3. Henry Wynn & Anatoly Zhigljavsky & Juan Romo, 1994. "The theory of search from a statistical viewpoint," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 1-45, December.
    Full references (including those not matched with items on IDEAS)

    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. Dennis Schmidt & Rainer Schwabe, 2015. "On optimal designs for censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 237-257, April.
    2. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    3. Pepelyshev, Andrey & Melas, Viatcheslav B. & Strigul, Nikolay & Dette, Holger, 2004. "Design of experiments for the Monod model : robust and efficient designs," Technical Reports 2004,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.
    5. Dette, Holger & O'Brien, Timothy E., 2003. "Efficient experimental design for the Behrens-Fisher problem with application to bioassay," Technical Reports 2003,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Harman, Radoslav & Jurík, Tomás, 2008. "Computing c-optimal experimental designs using the simplex method of linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 247-254, December.
    7. Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.
    8. Chiara Tommasi & Juan M. Rodríguez-Díaz & Jesús F. López-Fidalgo, 2023. "An equivalence theorem for design optimality with respect to a multi-objective criterion," Statistical Papers, Springer, vol. 64(4), pages 1041-1056, August.
    9. Dette, Holger & Martinez Lopez, Ignacio & Ortiz Rodriguez, Isabel M. & Pepelyshev, Andrey, 2004. "Efficient design of experiment for exponential regression models," Technical Reports 2004,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2006. "Optimal designs for free knot least squares splines," Technical Reports 2006,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Li, Guanghui & Zhang, Chongqi, 2017. "The pseudo component transformation design for experiment with mixture," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 19-24.
    12. Braess, Dietrich & Dette, Holger, 2004. "On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models," Technical Reports 2004,78, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    13. Lopez-Fidalgo, Jesus & Tommasi, Chiara, 2004. "Construction of MV- and SMV-optimum designs for binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 465-475, January.
    14. Dette, Holger & Pepelyshev, Andrey & Wong, Weng Kee, 2008. "Optimal designs for dose finding experiments in toxicity studies," Technical Reports 2008,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    15. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function," Technical Reports 2004,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    16. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    17. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    18. Rodríguez-Díaz, Juan M., 2017. "Computation of c-optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 287-296.
    19. Dette, Holger & Haines, Linda M. & Imhof, Lorens A., 2003. "Maximin and Bayesian optimal designs for regression models," Technical Reports 2003,10, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Dette, Holger & Biedermann, Stefanie & Pepelyshev, Andrey, 2004. "Some robust design strategies for percentile estimation in binary response models," Technical Reports 2004,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

    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:spr:jagbes:v:21:y:2016:i:4:d:10.1007_s13253-016-0259-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.