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Bayesian optimum designs for discriminating between models with any distribution

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  • Tommasi, C.
  • López-Fidalgo, J.

Abstract

The Bayesian KL-optimality criterion is useful for discriminating between any two statistical models in the presence of prior information. If the rival models are not nested then, depending on which model is true, two different Kullback-Leibler distances may be defined. The Bayesian KL-optimality criterion is a convex combination of the expected values of these two possible Kullback-Leibler distances between the competing models. These expectations are taken over the prior distributions of the parameters and the weights of the convex combination are given by the prior probabilities of the models. Concavity of the Bayesian KL-optimality criterion is proved, thus classical results of Optimal Design Theory can be applied. A standardized version of the proposed criterion is also given in order to take into account possible different magnitudes of the two Kullback-Leibler distances. Some illustrative examples are provided.

Suggested Citation

  • Tommasi, C. & López-Fidalgo, J., 2010. "Bayesian optimum designs for discriminating between models with any distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 143-150, January.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:143-150
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    References listed on IDEAS

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    1. J. López‐Fidalgo & C. Tommasi & P. C. Trandafir, 2007. "An optimal experimental design criterion for discriminating between non‐normal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 231-242, April.
    2. Martin-Martin, R. & Torsney, B. & Lopez-Fidalgo, J., 2007. "Construction of marginally and conditionally restricted designs using multiplicative algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5547-5561, August.
    3. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2008. "Improving updating rules in multiplicative algorithms for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 312-320, December.
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    2. Ghosh, Subir & Dutta, Santanu, 2013. "Robustness of designs for model discrimination," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 193-203.
    3. 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.
    4. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    5. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.
    6. Kira Alhorn & Holger Dette & Kirsten Schorning, 2021. "Optimal Designs for Model Averaging in non-nested Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 745-778, August.

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