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

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