## Monte Carlo implementation of Gaussian process
models for Bayesian regression and classification

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science,
University of Toronto**
Gaussian processes are a natural way of defining prior distributions
over functions of one or more input variables. In a simple
nonparametric regression problem, where such a function gives the mean
of a Gaussian distribution for an observed response, a Gaussian
process model can easily be implemented using matrix computations that
are feasible for datasets of up to about a thousand cases.
Hyperparameters that define the covariance function of the Gaussian
process can be sampled using Markov chain methods. Regression models
where the noise has a *t* distribution and logistic or probit models
for classification applications can be implemented by sampling as well
for latent values underlying the observations. Software is now
available that implements these methods using covariance functions
with hierarchical parameterizations. Models defined in this way can
discover high-level properties of the data, such as which inputs are
relevant to predicting the response.

Technical Report No. 9702, Dept. of Statistics (January 1997), 24 pages:
postscript, pdf,
associated software.

Also available
from arXiv.org.

**Associated reference:**
The following conference paper contains similar, and somewhat more
recent, material:
Neal, R. M. (1998) ``Regression and classification using Gaussian process
priors'' (with discussion), in J. M. Bernardo, *et al*
(editors) *Bayesian Statistics 6*, Oxford University Press,
pp. 475-501:
abstract,
postscript (without discussion),
pdf (without discussion),
associated software.