Bayesian Decision Making About Small Binomial Rates With Uncertainty About the Prior.

We address the problem of deciding between two actions related to the rate of faults in a process of manufacturing many identical items. The faults occur independently of each other and are rare, so that the binomial distribution of their count in a given period is well approximated by a Poisson. We use prior information in the form of a set of so-called plausible prior distributions to reflect the difficulties and uncertainty inherent in the process of capturing the expert's knowledge and opinions in a format amenable to a Bayesian analysis. Our analysis also incorporates an elicited set of plausible loss functions. [ABSTRACT FROM AUTHOR]