Related papers: Non-stationary Spatial Modeling Using Fractional S…
We propose a method for nonstationary covariance function modeling, based on the spatial deformation method of Sampson and Guttorp [1992], but using a low-rank, scalable deformation function written as a linear combination of the tensor…
We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…
A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is…
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…
Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and…
Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call…
Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…
Precipitation is a large-scale, spatio-temporally heterogeneous phenomenon, with frequent anomalies exhibiting unusually high or low values. We use Markov Random Fields (MRFs) to detect spatio-temporally coherent anomalies in gridded annual…
Spatial nonstationarity, the location variance of features' statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction…
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…
Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
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…