Related papers: Bayesian nonparametric generative modeling of larg…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

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…

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…

The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…

It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a…

A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

We provide theoretical procedures and practical recipes to simulate non-Gaussian correlated, homogeneous random fields with prescribed marginal distributions and cross-correlation structure, either in a N-dimensional Cartesian space or on…

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…

We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and…

Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…