UCSC-SOE-23-01: Multivariate Nearest-Neighbors Gaussian Processes with Random Covariance Matrices

Isabelle Grenier, Bruno Sanso and Jessica L. Matthews
01/19/2023 10:46 AM
We propose a non-stationary spatial model based on a normal-inverse-Wishart framework, conditioning on a set of nearest-neighbors. The model, called Nearest-Neighbor Gaussian Process with Random Covariance matrices (NN-RCM) is developed for both univariate and multivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. We illustrate the performance of the model with univariate and bivariate simulations, as well as with observations from two stationary satellites consisting of albedo measurements.