English
Related papers

Related papers: Transformed Gaussian Markov Random Fields and Spat…

200 papers

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…

Statistics Theory · Mathematics 2021-03-09 Helmut Harbrecht , Lukas Herrmann , Kristin Kirchner , Christoph Schwab

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…

Applications · Statistics 2017-10-03 Minjie Fan , Debashis Paul , Thomas C. M. Lee , Tomoko Matsuo

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…

Computation · Statistics 2018-02-08 Andrew Zammit-Mangion , Jonathan Rougier

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…

Numerical Analysis · Mathematics 2019-02-19 Jonas Latz , Marvin Eisenberger , Elisabeth Ullmann

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.,…

Statistics Theory · Mathematics 2007-06-13 Samuel Elogne , Dionisis Hristopulos

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…

Computer Vision and Pattern Recognition · Computer Science 2016-09-08 Zhirong Wu , Dahua Lin , Xiaoou Tang

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…

Methodology · Statistics 2016-03-09 Thomas Opitz

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…

Probability · Mathematics 2025-01-08 David Bolin , Alexandre B. Simas , Jonas Wallin

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…

Methodology · Statistics 2025-08-28 Matthias Herp , Johannes Brachem , Michael Altenbuchinger , Thomas Kneib

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…

Statistics Theory · Mathematics 2020-12-03 Likun Zhang , Benjamin A. Shaby , Jennifer L. Wadsworth

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…

Computation · Statistics 2019-11-18 Andee Kaplan , Mark S. Kaiser , Soumendra N. Lahiri , Daniel J. Nordman

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…

Robotics · Computer Science 2024-02-26 J. E. San Soucie , H. M. Sosik , Y. Girdhar

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…

Methodology · Statistics 2013-07-05 Xiangping Hu , Finn Lindgren , Daniel Simpson , Håvard Rue

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…

Statistics Theory · Mathematics 2014-11-04 Eunho Yang , Pradeep Ravikumar , Genevera I. Allen , Yulia Baker , Ying-Wooi Wan , Zhandong Liu

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…

Methodology · Statistics 2026-02-27 Johannes Brachem , Paul F. V. Wiemann , Matthias Katzfuss

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…

Applications · Statistics 2015-07-08 Zhixiang Lin , Tao Wang , Can Yang , Hongyu Zhao

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,…

Machine Learning · Statistics 2018-10-31 Ilya Soloveychik , Vahid Tarokh

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…

Methodology · Statistics 2025-11-14 Muyang Shi , Likun Zhang , Mark D. Risser , Benjamin A. Shaby

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…

Machine Learning · Statistics 2021-01-12 Sam Davanloo Tajbakhsh , Necdet Serhat Aybat , Enrique Del Castillo