Bayesian Specification and Identification of a Class of Mixture Models.

This note argues that a Bayesian framework is almost inescapable when specifying statistical models of the LISREL type, i.e. models involving not only latent and manifest variables but also incidental parameters. Indeed, a careful specification, making every hypothesis explicit and interpretable both contextually and statistically, requires a fully probabilistic framework, which is one of the most attractive features of the Bayesian approach. Such an environment allows one to develop a complete analysis of identification distinguishing five levels of identification problems.