ABSTRACT
This chapter seeks to identify the “optimal” reduction of a given experiment. The minimal sufficient σ-field may therefore be defined through the intersection of all completed sufficient σ-fields. Consequently, minimal sufficient σ-fields are essentially unique. In a Bayesian experiment, the sample information bears on a sufficient parameter only: conditionally on a sufficient parameter, the Bayesian experiment is totally non-informative. Identification theory is a domain in which Bayesian and classical methods treat nuisance parameters differently. Combining identification and exactness of a Bayesian experiment leads to the concept of a totally informative Bayesian experiment. In asymptotic theory, Bayesian consistency has generally been presented as the convergence of the posterior distributions to a point mass or a Dirac distribution, Berk, Hartigan.
