Parameter Curvature Revisted and the Bayes-frequentist divergence

Parameter curvature was introduced by Efron (1975) for classifying curved ex-
ponential models. We develop an alternative de nition that describes curvature
relative to location models. This modi ed curvature calibrates how Bayes poste-
rior probability di ers from familiar frequency based probability. And it provides
a basis for then correcting Bayes probabilities to agree with the reproducibil-
ity traditional to mainstream statistics. The two curvatures are compared and
examples are given.