zbMATH — the first resource for mathematics

Optimal Bayesian design for a logistic regression model: Geometric and algebraic approaches. (English) Zbl 0943.62029
Ghosh, Subir (ed.), Multivariate analysis, design of experiments, and survey sampling. A tribute to Jagdish N. Srivastava. New York, NY: Marcel Dekker. Stat., Textb. Monogr. 159, 609-624 (1999).
Introduction: L.M. Haines [J. R. Stat. Soc., Ser. B 57, No. 3, 575-598 (1995; Zbl 0827.62064)] and K. Chaloner [J. Stat. Plann. Inference 37, No. 2, 229-235 (1993; Zbl 0786.62073)] give closed-form results for Bayesian designs for nonlinear problems. Both papers use, among other examples, the logistic regression model with a known slope parameter. Both papers derive some of the same results for prior distributions with two points of support, but with very different methods. Haines uses a novel geometric approach and Chaloner uses a more traditional algebraic approach using an equivalence theorem. Prior distributions with a small number of support points are not of much practical use, but when closed-form solutions can be found they give an understanding of more general problems in which designs must be found numerically.
The two different approaches are compared and contrasted in Sections 2 and 3. A new result for a three-point prior distribution is given in Section 4, together with a discussion of the geometric approach. Some numerical results for multiple-point prior distributions are given in Section 5.
For the entire collection see [Zbl 0927.00053].

62F15 Bayesian inference
62K05 Optimal statistical designs
62J12 Generalized linear models (logistic models)
PDF BibTeX Cite