Bayesian Mixture Modeling by Monte Carlo Simulation

It is shown that Bayesian inference from data modeled by a mixture distribution can feasibly be performed via Monte Carlo simulation. This method exhibits the true Bayesian predictive distribution, implicitly integrating over the entire underlying parameter space. An innnite number of mixture components can be accommodated without diiculty, using a prior distribution for mixing proportions that selects a reasonable subset of components to explain any nite training set. The need to decide on a \correct" number of components is thereby avoided. The feasibility of the method is shown empirically for a simple classiication task.