Calibration, Sufficiency, and Domination Considerations for Bayesian Probability Assessors

DeGroot and Fienberg (1982a) recently considered various aspects of the problem of evaluating the performance of probability appraisers. After briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts. We then discuss some simple Bayesian mechanisms for making probability assessments and study their calibration, semicalibration, sufficiency, and domination properties. Finally, several results concerning the comparison of finite dichotomous experiments, relevant to the present work, are collected in an Appendix.