相关论文: Unifying Compactly Supported and Matern Covariance…
Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for…
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…
Matern correlation is of pivotal importance in spatial statistics and machine learning. This paper serves as a panoramic primer for this correlation with an emphasis on the exposition of its changing behavior and smoothness properties in…
The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…
Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…
In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…
In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to…
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…
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the…