A huge literature about clustering spatial time data exists. The problem has been studied both in a parametric and in a nonparametric setting. There are several problems in defining a proper clustering procedure, depending on the type of relationship between the clusters.

From a parametric point of view, a classic approach is to introduce mixture models and studying the posterior distribution of the mixture weights. We propose a mixture model where the mixing probabilities are time specific and are assumed to follow a Logistic-Normal distribution. We introduce dependence betweens the vectors of mixing probabilities by means of a Gaussian processes representation.

In a nonparametric setting, Dirichlet processes are often used, however how to introduce dependence between processes is still an open problem. The Dirichlet process may be extended in a hierarchical version, so that several processes share the same set of atoms with process-dependent weights, however the original construction of the hierarchical Dirichlet process considers independent processes. In this work we also propose a way to introduce dependence in the marginal distributions of the vectors of weights, by imposing a Gaussian copula whose correlation matrix has a given dependence structure (for instance, implying spatial-temporal dependence).