MIX: Bayesian inference for mixture models. The 'mix' programs implement Bayesian models for multivariate probability or probability density estimation that are based on finite or countably infinite mixtures. The countably infinite mixture models are equivalent to Dirichlet process mixtures. Each component of the mixture defines a joint probability or probability density for a set of target variables. At present, the targets must either all be binary or all be real-valued. For binary data, the targets are independent in the component distributions, with a "1" having some specified probability. For real-valued data, the targets are also independent in each of the component densities, each having a Gaussian distribution with some specified mean and standard deviation. The full distribution defined by the model is a mixture of these component distributions, with the weight of each component in the mixture being given by a set of component probabilities. The parameters of the component distributions (eg, the means and standard deviations for Gaussians) are given prior distributions, which may depend on "hyperparameters" that are themselves given priors. The mixing proportions are given a symmetric Dirichlet prior, with specified concentration parameter. In this implementation, these mixing proportions are not explicitly represented; all inference is instead done with the proportions integrated out. Sampling from the posterior distribution for the other parameters of the components and the hyperparameters is done using Markov chain methods. The resulting sample from the posterior can then be used to make predictions for future cases. The facilities supported by these programs are presently a bit rudimentary; mix-extensions.doc gives a list of things that could be done, but aren't yet. Copyright (c) 1997 by Radford M. Neal