A class of dependent Dirichlet processes via latent multinomial\n processes

We describe a procedure to introduce general dependence structures on a set\nof Dirichlet processes. Dependence can be in one direction to define a time\nseries or in two directions to define spatial dependencies. More directions can\nalso be considered. Dependence is induced via a set of latent processes and\nexploit the conjugacy property between the Dirichlet and the multinomial\nprocesses to ensure that the marginal law for each element of the set is a\nDirichlet process. Dependence is characterised through the correlation between\nany two elements. Posterior distributions are obtained when we use the set of\nDirichlet processes as prior distributions in a bayesian nonparametric context.\nPosterior predictive distributions induce partially exchangeable sequences\ndefined by generalised P\\'olya urs. A numerical example to illustrate is also\nincluded.\n