  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.
