# BUGS

We'll finish the course by looking at some general purpose software
for *Bayesian inference Using Gibbs Sampling*
(BUGS). Using BUGS (or WinBUGS, the fancy Microsoft Windows
version), one simply defines the model, the prior and the data,
and BUGS takes care of the rest. It implements a Gibbs sampling
scheme in whatever way it can, in order to produce samples from
the posterior distribution.
Work through the following examples, and then tackle the exercises
below.

### Exercises

- 1.
- Work through the first example and make sure you
understand what is going on.
- 2.
- Work through the second example. Get density
estimates and summary statistics for all of the
parameters. What is the posterior mean and variance of mu? What is the
posterior mean and variace of theta[2]?
- 3.
- Do the RATS example. Try and understand the model,
and what it is trying to achieve. What are the posterior means
and variances of the key parameters of the model?
- 4.
- Work through one or two other examples from Volume
1. See if you can figure out what is going on.