On probabilistic parametric inference

This paper formulates a theory of probabilistic parametric inference and explores the limits of its applicability. Unlike Bayesian statistical models, the system does not comprise prior probability distributions. Objectivity is imposed on the theory: a particular direct probability density should always result in the same posterior probability distribution. For calibrated posterior probability distributions it is possible to construct credible regions with posterior-probability content equal to the coverage of the regions, but the calibration is not generally preserved under marginalization. As an application of the theory, the paper also constructs a filter for linear Gauss–Markov stochastic processes with unspecified initial conditions.