Dependent Species Sampling Models for Spatial Density Estimation

Abstract

We consider a novel Bayesian nonparametric model for density estimation with an underlying spatial structure. The model is built on a class of species sampling models, which are discrete random probability measures that can be represented as a mixture of random support points and random weights. Specifically, we construct a collection of spatially dependent species sampling models and propose a mixture model based on this collection. The key idea is the introduction of spatial dependence by modeling the weights through a conditional autoregressive model. We present an extensive simulation study to compare the performance of the proposed model with competitors. The proposed model compares favorably to these alternatives. We apply the method to the estimation of summer precipitation density functions using Climate Prediction Center Merged Analysis of Precipitation data over East Asia.