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Non-Gaussian spatial and spatio-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines. FRK is an R package for spatial and spatio-temporal modeling and prediction with very large data sets that, to date, has only supported linear process models and Gaussian data models. In this paper, we describe a major upgrade to FRK that allows for non-Gaussian data to be analyzed in a generalized linear mixed model framework. These vastly more general spatial and spatio-temporal models are fitted using the Laplace approximation via the software TMB. The...

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 ...

Neural Bayes estimators are neural networks that approximate Bayes estimators. They are fast, likelihood-free, and amenable to rapid bootstrap-based uncertainty quantification. In this article, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of estimating parameters from replicated data, which we address using permutation-invariant neural networks. Through extensive simulation studies we demonstrate that neural Bayes estimat...

When analyzing environmental data, constructing a realistic statistical model is important, not only to fully characterize the physical phenomena, but also to provide valid and useful predictions. Gaussian process models are amongst the most popular tools used for this purpose. However, many assumptions are usually made when using Gaussian processes, such as stationarity of the covariance function. There are several approaches to construct nonstationary spatial and spatio-temporal Gaussian processes, including the deformation approach. In the deformation approach, the geographical domain is wa...

Conservationists in the Brazilian Amazon are using a new tool to predict the next sites of deforestation – and it may prove a gamechanger in the war on logging