Open AccessJournal Article
Towards Bayesian experimental design for nonlinear models that require a large number of sampling times
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TLDR
A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented.Abstract:
The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.read more
Citations
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A Review of Modern Computational Algorithms for Bayesian Optimal Design
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Bayesian Design of Experiments Using Approximate Coordinate Exchange
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References
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Book
Optimal Statistical Decisions
TL;DR: In this article, the authors present a survey of probability theory in the context of sample spaces and decision problems, including the following: 1.1 Experiments and Sample Spaces, and Probability 2.2.3 Random Variables, Random Vectors and Distributions Functions.
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Simulated Annealing: Theory and Applications
TL;DR: Performance of the simulated annealing algorithm and the relation with statistical physics and asymptotic convergence results are presented.
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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.