Analisi bayesiana di modelli "annidati" (Bayesian analysis of nested models)

We describe a Gibbs sampling algorithm for Bayesian analysis of mixtures models with a random number of components, and known components. For this problem (but in the more general case of unknown components), reversible jump MCMC techniques have been recently proposed (Richardson, Green, 1997). The difference between the two approaches is due to the choice of a different parametrization of the problem. This provides an example which shows how the choice of the parametrization also has implications on the computational techniques.