A Comparison of Two Elicitation Methods for a Prior Distribution for a Binomial Parameter

This paper compares two methods of elicitation for the hyperparameters of the conjugate beta distribution for a binomial sampling model. The PM (posterior mode) method of Chaloner and Duncan appears to be more sensitive to elicitation errors than does a new method proposed here. This new method uses the device of imaginary results, due to I. J. Good (Good, I. J. 1967. A Bayesian significance test for multinomial distributions. JRSSB 29 399--431 (with discussion).). An explicit model for elicitation errors is used in a simulation.