Conservative Bayes experimental design

Abstract

A major difficulty in applying Bayes methods is the potential for lack of objectivity when quantifying prior information. Existing Bayes design theory for acceptance/demonstration tests is heuristically examined for sensitivity of the design to changes in the prior distribution. The changes considered are associated with location and shape (information content) of the prior. The concept of a risk-conservative prior is developed as a means of controlling unintentional introduction of subjective prejudice in the choice of prior. The intuitive notion of conservatism in Bayes estimation (a broad flat prior has less influence than a more peaked prior) does not carry into design. It is shown that definition of a conservative prior in experimental design requires an understanding of the effects of changing the prior location and shape on the resulting Bayes risk, and conditional consumer and producer risks. A modified minimax principle is used to simplify prior choice. >