相关论文: Which Parameterization of the Mat\'ern Covariance …
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
A huge literature in statistics and machine learning is devoted to parametric families of correlation functions, where the correlation parameters are used to understand the properties of an associated spatial random process in terms of…
This paper studies Gaussian random fields with Mat\'ern covariance functions with smooth parameter $\nu>2$. Two cases of parameter spaces, the Euclidean space and $N$-dimensional sphere, are considered. For such smooth Gaussian fields, we…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Mat\'ern random fields are one of the most widely used classes of models in spatial statistics. The fixed-domain identifiability of covariance parameters for stationary Mat\'ern Gaussian random fields exhibits a dimension-dependent phase…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years,…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
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…
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…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
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…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…
Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…
Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
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…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…