Uncertainty Quantification Using the Nearest Neighbor Gaussian Process

Abstract

Gaussian process has been widely used in areas including geostatistics and uncertainty quantification due to its parsimonious yet flexible representation of a stochastic process. However, analyzing a large data set with Gaussian process can be challenging due to its O(n3) computational complexity, where n denotes the size of the data set. The recently proposed Nearest Neighbor Gaussian Process (NNGP) aims to approximate a Gaussian process with a target covariance function by using a series of conditional distributions and then exploiting the sparse precision matrices. We demonstrate that NNGP has the potential to be used for uncertainty quantification. We discover that when using NNGP to approximate a Gaussian process with strong smoothness, e.g., the squared-exponential covariance function, Bayesian inference needs to be carried out carefully with marginalizing over the random effects in NNGP. Using simulated and real data, we investigate empirically the performance of NNGP to approximate the squared-exponential covariance function as well as its ability to handle change-of-support effect, a common phenomenon in geostatistics and uncertainty quantification when only aggregated data over space are available.