Related papers: Transformed Gaussian Markov Random Fields and Spat…
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance operators. We consider centered GRFs given as variational…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
This paper addresses the inference of spatial dependence in the context of a recently proposed framework. More specifically, the paper focuses on the estimation of model parameters for a class of generalized Gibbs random fields, i.e.,…
Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic…
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…
For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important…
We present the Streaming Gaussian Dirichlet Random Field (S-GDRF) model, a novel approach for modeling a stream of spatiotemporally distributed, sparse, high-dimensional categorical observations. The proposed approach efficiently learns…
In this paper we propose a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) with oscillating covariance functions through systems of stochastic partial differential equations (SPDEs). We discuss how to build…
Spatial data are often derived from multiple sources (e.g. satellites, in-situ sensors, survey samples) with different supports, but associated with the same properties of a spatial phenomenon of interest. It is common for predictors to…
"Mixed Data" comprising a large number of heterogeneous variables (e.g. count, binary, continuous, skewed continuous, among other data types) are prevalent in varied areas such as genomics and proteomics, imaging genetics, national…
Quantifying uncertainty in future climate projections is hindered by the prohibitive computational cost of running physical climate models, which severely limits the availability of training data. We propose a data-efficient framework for…
In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…