Inner spike and slab Bayesian nonparametric models

Discrete Bayesian nonparametric models whose expectation is a convex linear combination of point mass at some the support and diffuse probability distribution allow to incorporate strong prior information, while still being extremely flexible. Recent contributions in statistical literature have successfully implemented such modelling strategy variety applications, including density estimation, regression model-based clustering. A thorough study presented on large class models, named inner spike slab hNRMI obtained by considering homogeneous normalized random measures with independent increments (hNRMI) base measure given distribution. In turn, distributional properties these are investigated, focus on: i) exchangeable partition function they induce, ii) number distinct values an sample, iii) posterior predictive distribution, iv) elements that coincide only positive probability. These theoretical findings represent main building block for actual implementation means generalized Pólya urn scheme.