Nonstationary Nearest Neighbor Gaussian Process: Hierarchical Model Architecture and MCMC Sampling

• Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Sébastien Coube-Sisqueille* and Sudipto Banerjee and Benoît Liquet
• Companies: Université de Pau et des Pays de l'Adour and University of California Los Angeles and Université de Pau et des Pays de l'Adour
• Keywords: Nearest Neighbor Gaussian Process; Nonstationary; Hierarchical model

Abstract

Nonstationary spatial modelling is exciting and potentially rewarding, but suffers from several problems : its computational cost, the complexity and lack of interpretability of multi-layered hierarchical models, and the difficulty of model selection. We tackle those problems by introducing a nonstationary Nearest Neighbor Gaussian Process (NNGP) model. NNGPs are a good starting point to address the problem of computational the cost because of their accuracy and affordability. We study the behavior of NNGPs that use a nonstationary covariance function, deriving some algebraic properties and exploring the impact of ordering on the effective covariance induced by NNGPs. To ease results analysis and model selection, we introduce a readable hierarchical model architecture. In particular, we make parameters interpretation and model selection easier by integrating stationary, circular and elliptic correlation in a consistent framework. We propose a MCMC algorithm based on Metropolis Adjusted Langevin Algorithm. We carry out experiments on synthetic data sets to find empirical practical rules.