Journal ArticleDOI
A Geometric Approach to Optimal Design for One‐Parameter Non‐Linear Models
TLDR
A geometric framework for constructing optimal Bayesian designs and maximin designs for non-linear models with a single unknown parameter and a prior distribution on that parameter, which is restricted in that it comprises exactly two points of support, is presented in this article.Abstract:
SUMMARY A geometric framework for constructing optimal Bayesian designs and maximin designs for non-linear models with a single unknown parameter and a prior distribution on that parameter, which is restricted in that it comprises exactly two points of support, is presented. The approach is illustrated by means of selected examples involving logistic regression and the simple exponential model, and its applicability to the construction of optimal designs for models with uncontrolled variation and to model robust designs is also demonstrated. In addition, the method is shown to provide some valuable insights into the general properties of optimal Bayesian designs for non-linear models.read more
Citations
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Journal ArticleDOI
Bayesian Experimental Design: A Review
TL;DR: This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models, and presents a uniied view of the topic by putting experimental design in a decision theoretic framework.
Journal ArticleDOI
Maximum entropy sampling and optimal Bayesian experimental design
Paola Sebastiani,Henry P. Wynn +1 more
TL;DR: Under suitable conditions, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions.
Journal ArticleDOI
Design Issues for Generalized Linear Models: A Review
TL;DR: A survey of various existing techniques dealing with the dependence problem is provided in this article, which includes locally optimal designs, sequential designs, Bayesian designs and quantile dispersion graph approach for comparing designs for generalized linear models.
Journal ArticleDOI
The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems
TL;DR: In this paper, the equivalence theorem for the Bayesian constrained design problem was proved for Bayesian nonlinear design problems with several objectives, including weighted and constrained design problems, and it was used to show that the results of Cook and Wong on equivalence of the weighted and bounded problems apply much more generally.
References
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Journal ArticleDOI
On the Mathematical Foundations of Theoretical Statistics
TL;DR: In this paper, the authors define the center of location as the abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling.
Book
Optimum experimental designs
Anthony C. Atkinson,A. N. Donev +1 more
TL;DR: In this article, the authors present an analysis of experiments with both qualitative and quantitative factors: Blocking response surface designs, restricted region designs, failure of the experiment and design augmentation, and discrimination between models.
Journal ArticleDOI
The Geometry of Mixture Likelihoods: A General Theory
TL;DR: In this paper, the existence, support size, likelihood equations, and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull.
Journal ArticleDOI
Locally Optimal Designs for Estimating Parameters
TL;DR: In this article, it was shown that locally optimal designs for large numbers of experiments can be approximated by selecting a certain set of randomized experiments and by repeating each of these randomized experiments in certain specified proportions.
Journal ArticleDOI
Optimal Bayesian design applied to logistic regression experiments
Kathryn Chaloner,Kinley Larntz +1 more
TL;DR: In this article, the authors derive a general theory for concave design critria for non-linear models and then apply the theory to logistic regression and propose designs which formally account for the prior uncertainty in the parameter values.