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. From this analysis the paper proceeds, on one hand, by giving some sficient conditions for the identification of the statistical model, and, on the other hand, by studying the identification problem in the predictive model