Unlike classical approaches, Bayesian methods enable expert opinion and objective information to augment data from an experiment, with the potential for more efficient designs and analysis. These advantages come at the expense of more sophisticated computing (to elicit priors and perform the analysis), and the methodology's apparent lack of objectivity relative to a frequentist approach. Robust Bayesian methods that perturb the prior or assess inferences for a class of priors have been developed to address the objectivity issue.

This presentation explores an alternate approach based on a partial characterization of the class of priors that, for a given data set, lead to a specific decision such as rejecting a point null hypothesis. These characterizations are intended to complement other Bayesian and frequentist data summaries. Non-parametric approaches based on moments and percentiles of the prior, and methods for parametric families such as the Gaussian and exponential with conjugate priors have been developed. The approach will be illustrated using monitoring data from a recent AIDS clinical trial.

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