Abstract

Operational statistics is an operational theory of probability and statistics which generalizes classical probability and statistics and provides a formalism particularly suited to the needs of quantum mechanics. Within this formalism, statistical inference can be accomplished using the Bayesian inference strategy. In a hierarchical Bayesian approach, a second-order probability measure, or credibility, represents degrees of belief in statistical hypotheses. A credibility determines an assignment of simple and conditioned betting rates to events in a natural way. In the setting of operational statistics, we show that a credibility is completely determined by the assignment of the betting rates it induces. This result suggests a certain unity between the Bayesian philosophy which deems that betting rates are central and the one which advocates the hierarchical approach