Nearest-Neighbor Geostatistical Models for Non-Gaussian Data

We develop a class of nearest neighbor mixture transition distribution process (NNMP) models that provides flexibility and scalability for non-Gaussian geostatistical data. We use a directed acyclic graph to define a proper spatial process with finite-dimensional distributions given by finite mixtures. We develop conditions to construct general NNMP models with pre-specified stationary marginal distributions. We also establish lower bounds for the strength of the tail dependence implied by NNMP models, demonstrating the flexibility of the proposed methodology for modeling multivariate dependence through bivariate distribution specification. To implement inference and prediction, we formulate a Bayesian hierarchical model for the data, using the NNMP prior model for the spatial random effects process. From an inferential point of view, the NNMP model lays out a new computational approach to handling large spatial data sets, leveraging the mixture model structure to avoid computational issues that arise from large matrix operations. We illustrate the benefits of the NNMP modeling framework using synthetic data examples and through analysis of sea surface temperature data from the Mediterranean sea.