Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

By Abhirup Datta, Sudipto Banerjee, Andrew O. Finley, Alan E. Gelfand. Journal of the American Statistical Association, 2014

749 citations recorded by the source corpus.

Abstract Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

Subfields: Environmental Engineering, Nature and Landscape Conservation

View Paper: https://www.semanticscholar.org/paper/cc2c6f6cdebe03c9e5f2564ca6e53e24db7f1667

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Environmental Engineering

In Nature and Landscape Conservation

Citations in the corpus

Random Forests for dependent data (2020, methodology): “In particular, Nearest Neighbor Gaussian Processes [15, 27, 16, 17] has emerged as a leading candidate.”
Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes (2015, methodology): “t ˙T t=0 ! falls into the class of skew normal distributions presented in Section 4.1. In the cases K+ is too large, we suggest a combination of the following: i) use approximations such as the NNGP (Datta et al., 2016) ; ii) sample βK in blocks of times to achieve reasonable dimension. Block β−K is”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, background): “In contrast, transductive NLE, e.g., the nearest-neighbors (NeNe) [112] which could induce a valid stochastic process [108], [113], employs a dynamic partition to choose m 0 neighbor points around x ∗ , resulting in O ( n t m 30 ) complexity that relies on the test size n t . issue A key in…”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, methodology): “To further improve on these issues, other methods that have been recently developed include the nearest-neighbor Gaussian process models [18], multiresolution Gaussian process models [51], equivalent kriging [40], multi-level restricted Gaussian maximum likelihood estimators [16], and hierarchical l”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, background): “The NNGP (Datta et al., 2016a,b,c) considers explicit data models (such as the additive Gaussian noise assumed here), and conditions only on latent variables: q y ( i ) = q ( i ) and q z ( i ) = ∅ .”