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Finding near-optimal Bayesian experimental designs via genetic algorithms. (English) Zbl 1182.62156
Summary: This article shows how a genetic algorithm can be used to find near-optimal Bayesian experimental designs for regression models. The design criterion considered is the expected Shannon information gain of the posterior distribution obtained from performing a given experiment compared with the prior distribution. Genetic algorithms are described and then applied to experimental designs. The methodology is then illustrated with a wide range of examples: linear and nonlinear regression, single and multiple factors, and normal and Bernoulli distributed experimental data.
MSC:
62K05Optimal statistical designs
62C10Bayesian problems; characterization of Bayes procedures
62J12Generalized linear models
62B10Statistical information theory
90C59Approximation methods and heuristics
62F15Bayesian inference