EXAMPLES OF BAYESIAN MODELING WITH NEURAL NETWORKS AND GAUSSIAN PROCESSES

This section shows how Bayesian inference for models based on neural
networks and Gaussian processes can be done for three simple synthetic
problems.

The output shown below was obtained by running the software on our
machine, with ">" at the start of a line indicating a command line
that was input.  It is possible (even likely) that your results will
differ, even if you have installed the software correctly, since small
differences in floating point arithmetic can be magnified into large
differences in the course of the simulation.  However, unless one of
the simulations became stuck in an isolated local mode, the final
predictions you obtain from 'net-pred' for 'gp-pred' should be close
to those reported below.

All the data sets mentioned here are present in the 'examples'
sub-directory, along with the C source of the programs that generated
them.  It is assumed below that you have changed to this directory.
The command sequences for running the simulations that are mentioned
below are also stored in this directory, in shell files with the names
'rcmds.net', 'rcmds.gp', 'bcmds.net', 'bcmds.gp', 'ccmds.net', and
'ccmds.gp'.

Note that the particular network architectures, priors, and Markov
chain sampling options used below are only examples of reasonable
choices.  There are many other possibilities that are also reasonable.
To gain a full understanding of the various possibilities, and their
advantages and disadvantages, you will need to read both the general
references given earlier for these models, and the detailed
documentation in the ".doc" files.