Bayesian epistemic values: focus on surprise, measure probability!

The e-value or epistemic value, ev(H), measures the statistical significance of H, a hypothesis about the parameter θ of a Bayesian model. The e-value is obtained by a probability-possibility transformation of the model’s posterior measure, p(θ), and can, in turn, be used to define the FBST or Full Bayesian Significance Test. This article investigates the relation of this novel approach to more standard probability-possibility transformations. In particular, we show how and why the e-value focus on or conforms with s(θ) = p(θ)/r(θ), the model’s surprise function relative to the reference density r(θ), while it keeps itself consistent with the model’s posterior probability measure. In addition we investigate traditional objections raised in decision theoretic Bayesian statistics against measures of significance engendered by probability-possibility transformations.