66,104 research outputs found
Optimal Discrimination Designs for Exponential Regression Models
We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw (1995) or Gibaldi and Perrier (1982). We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory?s Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach. --Compartmental Model,Model Discrimination,Discrimination Design,Locally Optimal Design,Robust Optimal Design,Maximin Optimal Design
Optimal discrimination designs for exponential regression models
We investigate optimal designs for discriminating between exponential regression models
of different complexity, which are widely used in the biological sciences; see, e.g.,
Landaw (1995) or Gibaldi and Perrier (1982). We discuss different approaches for the
construction of appropriate optimality criteria, and find sharper upper bounds on the
number of support points of locally optimal discrimination designs than those given by
Caratheodory’s Theorem. These results greatly facilitate the numerical construction of
optimal designs. Various examples of optimal designs are then presented and compared
to different other designs. Moreover, to protect the experiment against misspecifications
of the nonlinear model parameters, we adapt the design criteria such that the resulting
designs are robust with respect to such misspecifications and, again, provide several
examples, which demonstrate the advantages of our approach
Robust T-optimal discriminating designs
This paper considers the problem of constructing optimal discriminating
experimental designs for competing regression models on the basis of the
T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975)
57-70]. T-optimal designs depend on unknown model parameters and it is
demonstrated that these designs are sensitive with respect to misspecification.
As a solution to this problem we propose a Bayesian and standardized maximin
approach to construct robust and efficient discriminating designs on the basis
of the T-optimality criterion. It is shown that the corresponding Bayesian and
standardized maximin optimality criteria are closely related to linear
optimality criteria. For the problem of discriminating between two polynomial
regression models which differ in the degree by two the robust T-optimal
discriminating designs can be found explicitly. The results are illustrated in
several examples.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1117 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bayesian T-optimal discriminating designs
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 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.Comment: 25 pages, 3 figure
Model selection via Bayesian information capacity designs for generalised linear models
The first investigation is made of designs for screening experiments where
the response variable is approximated by a generalised linear model. A Bayesian
information capacity criterion is defined for the selection of designs that are
robust to the form of the linear predictor. For binomial data and logistic
regression, the effectiveness of these designs for screening is assessed
through simulation studies using all-subsets regression and model selection via
maximum penalised likelihood and a generalised information criterion. For
Poisson data and log-linear regression, similar assessments are made using
maximum likelihood and the Akaike information criterion for minimally-supported
designs that are constructed analytically. The results show that effective
screening, that is, high power with moderate type I error rate and false
discovery rate, can be achieved through suitable choices for the number of
design support points and experiment size. Logistic regression is shown to
present a more challenging problem than log-linear regression. Some areas for
future work are also indicated
Optimal discrimination designs
We consider the problem of constructing optimal designs for model
discrimination between competing regression models. Various new properties of
optimal designs with respect to the popular -optimality criterion are
derived, which in many circumstances allow an explicit determination of
-optimal designs. It is also demonstrated, that in nested linear models the
number of support points of -optimal designs is usually too small to
estimate all parameters in the extended model. In many cases -optimal
designs are usually not unique, and in this situation we give a
characterization of all -optimal designs. Finally, -optimal designs are
compared with optimal discriminating designs with respect to alternative
criteria by means of a small simulation study.Comment: Published in at http://dx.doi.org/10.1214/08-AOS635 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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