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Bayesian optimal designs for multi-factor nonlinear models

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  • Lei He

    (Anhui Normal University)

Abstract

This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian $$\varPsi _q$$ Ψ q -optimality criterion proposed by Dette et al. (Stat Sinica 17:463–480, 2007) is considered. It is shown that the product-type designs are optimal for the additive multi-factor nonlinear models with or without constant term when the proposed sufficient conditions are satisfied. Some examples of application using the exponential growth models with several variables are presented to illustrate optimal designs based on the Bayesian $$\varPsi _q$$ Ψ q -optimality criterion considered.

Suggested Citation

  • Lei He, 2021. "Bayesian optimal designs for multi-factor nonlinear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 223-233, March.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00522-w
    DOI: 10.1007/s10260-020-00522-w
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    References listed on IDEAS

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    1. Carmelo Rodríguez & Isabel Ortiz & Ignacio Martínez, 2016. "A-optimal designs for heteroscedastic multifactor regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 757-771, February.
    2. S. Biedermann & H. Dette & D. C. Woods, 2011. "Optimal design for additive partially nonlinear models," Biometrika, Biometrika Trust, vol. 98(2), pages 449-458.
    3. He, Lei, 2018. "Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 201-208.
    4. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
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