  Dirichlet processes and their extensions have reached a great popularity in
Bayesian nonparametric statistics. They have also been introduced for spatial
and spatio-temporal data, as a tool to analyze and predict surfaces. A popular
approach to Dirichlet processes in a spatial setting relies on a stick-breaking
representation of the process, where the dependence over space is described in
the definition of the stick-breaking probabilities. Extensions to include
temporal dependence are still limited, however it is important, in particular
for those phenomena which may change rapidly over time and space, with many
local changes. In this work, we propose a Dirichlet process where the
stick-breaking probabilities are defined to incorporate both spatial and
temporal dependence. We will show that this approach is not a simple extension
of available methodologies and can outperform available approaches in terms of
prediction accuracy. An advantage of the method is that it offers a natural way
to test for separability of the two components in the definition of the
stick-breaking probabilities.
