Bayesian optimum designs for discriminating between models with any distribution

Tommasi, Chiara; López–Fidalgo, Jesús

doi:10.1016/j.csda.2009.07.022

Cited by 38 publications

(23 citation statements)

References 15 publications

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“…Recent work allows errors in the models to be non-normally distributed but still requires the specification of the mean structures. This research is motivated by the interesting work of Otsu (2008) to discriminate among semi-parametric models by generalizing the KL-optimality criterion proposed by López-Fidalgo et al (2007) and Tommasi and López-Fidalgo (2010). In our work we provide further important insights in this interesting optimality criterion.…”

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confidence: 86%

Optimal discrimination designs for semiparametric models

et al. 2017

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Much of the work in the literature on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters in some models. Recent work allows errors in the models to be non-normally distributed but still requires the specification of the mean structures. This research is motivated by the interesting work of Otsu (2008) to discriminate among semi-parametric models by generalizing the KL-optimality criterion proposed by López-Fidalgo et al. (2007) and Tommasi and López-Fidalgo (2010). In our work we provide further important insights in this interesting optimality criterion. In particular, we propose a practical strategy for finding optimal discrimination designs among semi-parametric models that can also be verified using an equivalence theorem. In addition, we study properties of such optimal designs and identify important cases where the proposed semi-parametric optimal discrimination designs coincide with the celebrated T -optimal designs.

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confidence: 86%

Optimal discrimination designs for semiparametric models

et al. 2017

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“…, η ν , where the parameter θ 1 has the same meaning as before. As pointed out by Tommasi and López-Fidalgo (2010) and Braess and Dette (2013) there are many situations, where it is not clear which model should be considered as fixed and these authors proposed a symmetrized Bayesian (instead of minimax) version of the T -optimality criterion, that is…”

Section: T -Optimal Designsmentioning

confidence: 99%

Bayesian $T$-optimal discriminating designs

Dette¹,

Melas²,

Guchenko³

2015

Ann. Statist.

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The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T-optimality criterion introduced by Atkinson and Fedorov (1975a) is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail.

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“…Because of its importance this problem has a long history. Early work dates back to Box and Hill (1967); Stigler (1971); Atkinson and Fedorov (1975) who determined optimal designs for model discrimination byroughly speaking -maximizing the power of a test between competing regression models [see also Ucinski and Bogacka (2005); López-Fidalgo et al (2007); Wiens (2009); Dette and Titoff (2009) or Tommasi and López-Fidalgo (2010) for some more recent references]. A different line of research in this context was initiated by Läuter (1974) who proposed a criterion based on a product of the determinants of the information matrices in the various models under consideration, which yields efficient designs for all models under consideration.…”

Section: Introductionmentioning

confidence: 99%

Optimal designs for frequentist model averaging

2019

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We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the asymptotic mean squared error of the frequentist model averaging estimate by the choice of an experimental design. Necessary conditions for the optimal solution of a locally and Bayesian optimal design problem are established. The results are illustrated in several examples and it is demonstrated that Bayesian optimal designs can yield a reduction of the mean squared error of the model averaging estimator up to 45%.

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Bayesian optimum designs for discriminating between models with any distribution

Cited by 38 publications

References 15 publications

Optimal discrimination designs for semiparametric models

Optimal discrimination designs for semiparametric models

Bayesian $T$-optimal discriminating designs

Optimal designs for frequentist model averaging

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