Nearest-Neighbor Mixture Models for Non-Gaussian Spatial Processes

Abstract: We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional independence in representing a multivariate distribution through factorization into a product of univariate conditionals, and is extended to a full spatial process. We model each conditional as a mixture of spatially varying transition kernels, with locally adaptive weights, for each one of a given number of nearest neighbors. The modeling framework emphasizes the description of non-Gaussian dependence at the data level, in contrast with approaches that introduce a spatial process for transformed data, or for functionals of the data probability distribution. Thus, it facilitates efficient, full simulation-based inference. We study model construction and properties analytically through specification of bivariate distributions that define the local transition kernels, providing a general strategy for modeling general types of non-Gaussian data. Regarding computation, the framework lays out a new approach to handling spatial data sets, leveraging a mixture model structure to avoid computational issues that arise from large matrix operations. We illustrate the methodology using synthetic data examples and an analysis of Mediterranean Sea surface temperature observations.