Methods are developed for eliciting a Dirichlet prior based upon stating bounds on the individual probabilities that hold with high prior probability. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated how to assess the prior with respect to the bias it induces as well as how to check for prior-data conflict. It is shown that the assessment of ...

Abstract If a prior probability does not exist or is controversial, can we formulate probabilistic inference based only on the properties of the measurement? In the case of plain ‘location’ measurements the answer to this is known. Here we extend that answer to address the general problem of estimating a scalar parameter from a small data sample. That measurement is treated as if resulting from...