Related papers: Accounting for Multiple Covariates in Non-Stationa…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
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…
Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
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…
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…
Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…
Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence in the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the…
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…
In this paper we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify…
Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
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…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
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…
Modeling the joint distribution of extreme weather events in multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…