    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.

                Copyright (c) 1995-2003 by Radford M. Neal