A scalable Bayesian nonparametric model for large spatio-temporal data

Abstract

The Bayesian nonparametric (BNP) approach is an effective tool for building flexible spatio-temporal probability models. Despite the flexibility and attractiveness of this approach, the resulting spatio-temporal models become computationally demanding when datasets are large. This paper develops a class of computationally efficient and easy to implement BNP models for large spatio-temporal data. To be more specific, we introduce a random distribution for the spatio-temporal effects based on a stick-breaking construction in which the atoms are modeled in terms of a basis system. In this framework, a low rank basis approximation and a vector autoregressive process are used to model spatial and temporal dependencies, respectively. We demonstrate that the proposed model is an extension of the Gaussian low rank model with similar computational complexity, hence it offers great scalability for large spatio-temporal data. Through a simulation study, we assess the performance of the proposed model. For illustration, we then analyze a set of data comprised of precipitation measurements.