Dirichlet processes and their extensions are very popular in Bayesian nonparametric statistics. It has also been introduced to spatial and spatiotemporal data as a tool for analyzing and predicting surfaces. A common approach to Dirichlet processes in a spatial setting relies on a rod-like failure representation of the process, and the dependence on space is described in the definition of the rod-like failure probability. Extensions involving temporal dependencies are still limited, but are particularly important for phenomena that can change rapidly over time and space, with many local changes. In this work, we propose a Dirichlet process in which the stick-breaking probability is defined to incorporate both spatial and temporal dependencies. Rather than being a simple extension of available methodologies, we show that this approach outperforms available approaches in terms of predictive accuracy. The advantage of this method is that he provides a natural way to test the separability of two components in the definition of the stick breaking probability.

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