Related papers: Non-stationary Spatial Modeling Using Fractional S…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
Gaussian processes (GPs) and Gaussian random fields (GRFs) are essential for modelling spatially varying stochastic phenomena. Yet, the efficient generation of corresponding realisations on high-resolution grids remains challenging,…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…
Precipitation exceedance probabilities are widely used in engineering design, risk assessment, and floodplain management. While common approaches like NOAA Atlas 14 assume that extreme precipitation characteristics are stationary over time,…
Gaussian random fields (GRF) are a fundamental stochastic model for spatiotemporal data analysis. An essential ingredient of GRF is the covariance function that characterizes the joint Gaussian distribution of the field. Commonly used…
This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new…
Observations of groundwater pollutants, such as arsenic or Perfluorooctane sulfonate (PFOS), are riddled with left censoring. These measurements have impact on the health and lifestyle of the populace. Left censoring of these spatially…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…
Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…
Conditional probabilistic graphical models provide a powerful framework for structured regression in spatio-temporal datasets with complex correlation patterns. However, in real-life applications a large fraction of observations is often…
Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under…
Metric graphs are useful tools for describing spatial domains like road and river networks, where spatial dependence act along the network. We take advantage of recent developments for such Gaussian Random Fields (GRFs), and consider joint…
In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…
The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and…
There are many situations when modelling environmental phenomena for which it is not appropriate to assume a stationary dependence structure. \cite{sampson1992} proposed an approach to allowing nonstationarity in dependence based on a…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…