Bayesian Nonparametric Modeling based on Species Sampling Models

Abstract

In this dissertation we propose Bayesian nonparametric models for the inference of spatially varying densities based on mixtures of dependent species sampling models. The species sampling model is a discrete random probability distribution represented as the sum of the random support points with random weights. The spatial dependency is introduced by modeling the weights through the conditional autoregressive model. The proposed models are illustrated in two simulated data sets and show better performance than competitors based on a Dirichlet process or where dependence is not incorporated. The proposed method is also applied to real data sets.