I'm trying to build a generative model to run a Monte Carlo simulation. The existing data consist of a combination of discrete and continuous variables. Suppose I have a number of people...
Age Sex Non-white 21 1 1 35 1 1
I can easily use a mixture of Gaussians to model this data set and just use EM to estimate the mixture coefficients. But I'm not sure if the underlying assumptions are sound when the underlying components of the joint aren't necessarily (or at all) Gaussian.
I know a couple of more complicated methods, such as using Bayesian networks or things coming out of machine learning (e.g. Boltzmann Machines), but I doubt that they'll be useful for my rather small data set.
I am wondering if there's a compact way to build generative models of multivariate, correlated categorical variables. Or is mixture of Gaussians generally sufficient?