    EXAMPLES OF MARKOV CHAIN SAMPLING FOR SIMPLE BAYESIAN MODELS

    The 'dist' programs can be used to sample from the posterior
    distribution of the parameters of a Bayesian model, specified by
    giving formulas for minus the log of the prior distribution, and for
    minus the log likelihood for one case.  The model defines the
    conditional distribution of one or more "target" values in a case,
    given the values of the "inputs" for that case.  The cases are
    independent of each other.

    Models of this sort can handle regression and classification problems,
    in which the "targets" are the response variables and the "inputs" the
    predictor variables.  When the number of inputs is zero, the models
    will estimate the joint probability or probability density of the
    target values.  However, the set of allowed models is restricted by
    the range of formulas supported, as well as by the present restriction
    to no more than 10 inputs and 10 targets per case.  Also, latent
    variables cannot be explicitly represented at present, though some
    latent variable models can be defined by summing over the possible
    latent values in the likelihood.  The facilities of this module are
    meant primarily as a way of demonstrating the Markov chain sampling
    methods on statistical problems, not as a comprehensive statistical
    modeling package.

    These examples also illustrate some of the Markov chain sampling
    facilities not demonstrated earlier.  The linear regression example
    (Ex-bayes-r.doc) illustrates the use of "windows" with hybrid Monte
    Carlo.  The t-distribution example (Ex-bayes-t.doc) shows how one can
    set stepsizes differently for different variables.  The example of
    probability estimation for categorical data (Ex-bayes-p.doc) shows how
    the marginal likelihood for a model (more generally, the normalizing
    constant for the distribution) can be found using Annealed Importance
    Sampling.

    The data and command files for these examples are in the "ex-bayes"
    directory.