Finding near-optimal Bayesian experimental designs via genetic algorithms. (English) Zbl 1182.62156

Hamada, M.; Martz, H. F.; Reese, C. S.; Wilson, A. G.

Am. Stat. 55, No. 3, 175-181 (2001).

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:

62K05	Optimal statistical designs
62C10	Bayesian problems; characterization of Bayes procedures
62J12	Generalized linear models (logistic models)
62B10	Statistical aspects of information-theoretic topics
90C59	Approximation methods and heuristics in mathematical programming
62F15	Bayesian inference

Keywords:

expected information gain; logistic regression; linear and nonlinear regression; multifactor designs; Shannon information

Software:

tsbridge