  Nonparametric Bayesian approaches based on Gaussian processes have recently
become popular in the empirical learning community. They encompass many
classical methods of statistics, like Radial Basis Functions or various
splines, and are technically convenient because Gaussian integrals can be
calculated analytically. Restricting to Gaussian processes, however, forbids
for example the implemention of genuine nonconcave priors. Mixtures of Gaussian
process priors, on the other hand, allow the flexible implementation of complex
and situation specific, also nonconcave "a priori" information. This is
essential for tasks with, compared to their complexity, a small number of
available training data. The paper concentrates on the formalism for Gaussian
regression problems where prior mixture models provide a generalisation of
classical quadratic, typically smoothness related, regularisation approaches
being more flexible without having a much larger computational complexity.
