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.