10 Nearest Neighbor Gaussian Process Variational Inference for Large Geostatistical Datasets

Oregon Convention Center 

With the substantial increase in the availability of geostatistical data, statisticians are now equipped to make inference on spatial covariance from large datasets, which is critical in understanding spatial dependence. Traditional methods, such as Markov Chain Monte Carlo (MCMC) sampling within a Bayesian framework, can become computationally expensive as the number of spatial locations increases. As an important alternative to MCMC, Variational Inference approximates the posterior distribution through optimization. In this paper, we propose a nearest neighbor Gaussian process variational inference (NNGPVI) method to approximate the posterior. This method introduces nearest-neighbor-based sparsity in both the prior and the approximated posterior distribution. Doubly stochastic gradient methods are developed for the implementation of the optimization process. Our simulation studies demonstrate that NNGPVI achieves comparable accuracy to MCMC methods but with reduced computational costs. An analysis of satellite temperature data illustrates the practical implementation of NNGPVI and shows the inference results are matched with those obtained from the MCMC approach.

Bayesian Modeling

Spatial Statistics

Variational Inference

Gaussian Process

Nearest Neighbor 

Section on Bayesian Statistical Science