Models specified by unnormalized densities are a problem for Bayesian
inference because if the
model is specified by a family of unnormalized densities 
having a normalizing function
that is analytically intractable, then the likelihood
is also analytically intractable. Hence the joint density of data and parameter
is analytically intractable. Dealing with such families satisfactorily seems to be an open research question.
This issue has been obscured by the remarkable progress in Bayesian inference using MCMC in recent years. No one points out that likelihood inference is still easier than Bayesian inference in most situations. Many models for which exact likelihood inference is easy, generalized linear models, for example, require MCMC to carry out Bayesian inference. Many models for which MCMC likelihood inference is routine, have another level of difficulty when Bayesian inference is tried and are still open research problems. All of the likelihood analysis in this chapter is an example of this phenomenon.