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Optimal Bayesian design applied to logistic regression experiments. (English) Zbl 0666.62073
A traditional way to design a binary response experiment is to design the experiment to be most efficient for a best guess of the parameter values. A design which is optimal for a best guess however may not be efficient for parameter values close to that best guess. We propose designs which formally account for the prior uncertainty in the parameter values. A design for a situation where the best guess has substantial uncertainty attached to it is very different from a design for a situation where approximate values of the parameters are known.
We derive a general theory for concave design criteria for non-linear models and then apply the theory to logistic regression. Designs found by numerical optimization are examined for a range of prior distributions and a range of criteria. The theoretical results are used to verify that the designs are indeed optimal.

MSC:
62K05 Optimal statistical designs
62F15 Bayesian inference
Software:
AS 47
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