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"Modeling Big, Heterogeneous, Non-Gaussian Spatial and Spatio-Temporal " by Matthew Sainsbury-Dale, Andrew Zammit- Mangion et al.

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 existing functionality of FRK is retained with this advance into non-Gaussian models; in particular, it allows for automatic basis-function construction, it can handle both point-referenced and areal data simultaneously, and it can predict process values at any spatial support from these data. This new version of FRK also allows for the use of a large number of basis functions when modeling the s ....

Areal Data , Basis Functions , Big Data , Hange Of Support , Ixed Rank Kriging , On Gaussian Data , Spatial Statistics ,

"Nearest-Neighbor Mixture Models for Non-Gaussian Spatial Processes" by Xiaotian Zheng, Athanasios Kottas et al.

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 direct spatial modeling of non-Gaussian data, in contrast with approaches that introduce a spatial process for transformed data, or for functionals of the data probability distribution. We study model construction and properties analytically through specification of bivariate distributions that define the local transition kernels. This provides a general strategy for modeling different types of no ....

Mediterranean Sea , Oceans General , Bayesian Hierarchical Models , Markov Chain Monte Carlo , Spatial Statistics , Ail Dependence ,

"Likelihood-Free Parameter Estimation with Neural Bayes Estimators" by Matthew Sainsbury-Dale, Andrew Zammit-Mangion et al.

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 estimators can be used to quickly estimate parameters in weakly identified and highly parameterized models with relative ease. We illustrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second. ....

Red Sea , Djibouti General , Amortized Inference , Deep Learning , Xchangeable Data , Xtreme Value Model , Ermutation Invariant , Oint Estimation , Spatial Statistics ,

"Deep Statistical Models with Application to Environmental Data" by Quan Vu

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 warped into a new domain, on which the Gaussian process is modeled to be stationary. One of the main challenges with this approach is how to construct a deformation function that is complicated enough to adequately capture the nonstationarity in the process, but simple enough to facilitate statistical inference and prediction. In this thesis, by using ideas from deep learning, we construct deformati ....

Monte Carlo , Gaussian Process , Spatial Statistics ,

Could AI save the Amazon rainforest?

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 ....

Rio De Janeiro , Estado Do Rio , Mato Grosso Do Sul , Fundo Vale , Juliano Assun , Arthur Cezar Pinheiro Leite , Carlos Souza Jr , Climate Policy Initiative , Environmental Protection Area , Brazilian Amazon , Deforestation Alert System , Spatial Statistics , Pontifical Catholic University , Godofredo Pires ,