Fiducial estimates of unknown probabilities

Abstract

The much debated fiducial argument, developed by R.A.Fischer in the thirties, makes the inductive reasoning possible even on the basis of a single sample observation. It allows, when suitably adapted, to describe a personal uncertainty about a probability value (not approximate by an empirical frequency) through second order probability distributions: the proposed models, arisen from the application of fiducial principles to suitable probability transforms (odds and log-odds), required in fact solely a subjective starting evaluation of the unknown probability.