Consistency and identifiability in Bayesian analysis

Abstract

The importance of posterior consistency in the robustness of Bayesian analysis is examined and discussed. The notions of sufficient and minimal sufficient parameters are introduced and important consistency results for such parameters are derived. We see that minimal sufficient parameters are fundamental in characterising the relationship between data and parameters. The concept of identifiability is then introduced and several equivalent definitions are given. The relationship between consistency and identifiability is examined and means of establishing identifiability are examined with a view to finding useful practical tests of identifiability. These results are applied to a simple example involving non response.