Uncertainty reduction in a class of dependent Dirichlet processes

We consider a dependent Dirichlet process model driven by a Fleming–Viot diffusion, with observations collected at discrete time points in a Hidden Markov model fashion. We investigate empirically a phenomenon described in [2], whereby upon conditioning the underlying random probability measure on data collected at past and future times, the mixture distribution which describes the posterior distribution of the random measure benefits from an automatic reduction of the number of components. This reduction depends on the observed multiplicities and upweights components which feature observations that are shared across multiple times, and is bound to have positive implications for inference in terms of reduction of the estimation uncertainty and computational cost.