Trade-off sensitive experimental design: a multicriterion, decision theoretic, Bayes linear approach. (English) Zbl 1077.62059
Summary: We show how mutually utility independent hierarchies, which weigh the various costs of an experiment against benefits expressed through a mixed Bayes linear utility representing the potential gains in knowledge from the experiment, provide a flexible and intuitive methodology for experimental design which remains tractable even for complex multivariate problems. A key feature of the approach is that we allow imprecision in the trade-offs between the various costs and benefits. We identify the Pareto optimal designs under imprecise specification and suggest a criterion for selecting between such designs. The approach is illustrated with respect to an experiment related to the oral glucose tolerance test.
MSC:
| 62K05 | Optimal statistical designs |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
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