Dependent Mixtures of Geometric Weights Priors

Abstract: A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking processes. This approach is based on a new random central masses version of the Pairwise Dependent Dirichlet Process prior mixture model (PDDP) first introduced in Hatjispyros et al. (2011). The idea is to create pairwise dependence through random measures that are location-preserving-expectations of Dirichlet random measures. Our contention is that mixture modeling with Pairwise Dependent Geometric Stick Breaking Process (PDGSBP) priors is sufficient for prediction and estimation purposes; moreover the associated Gibbs sampler is much faster and easier to implement than its Dirichlet Process based counterpart. To this respect, we provide a-priori-synchronized comparison studies under sparse $m$-scalable synthetic and real data examples.