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With the advancement of technology and the arrival of miniaturized environmental sensors that offer greater performance, the idea of building mobile network sensing for air quality has quickly emerged to increase our knowledge of air…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
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…
Informative sampling designs can impact spatial prediction, or kriging, in two important ways. First, the sampling design can bias spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Second, even with…
Spatially misaligned data, where the response and covariates are observed at different spatial locations, commonly arise in many environmental studies. Much of the statistical literature on handling spatially misaligned data has been…
We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$…
Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the…
Accurate spatial interpolation of the air quality index (AQI), computed from concentrations of multiple air pollutants, is essential for regulatory decision-making, yet AQI fields are inherently non-Gaussian and often exhibit complex…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
Spatial misalignment arises when datasets are aggregated or collected at different spatial scales, leading to information loss. We develop a Bayesian disaggregation framework that links misaligned data to a continuous-domain model through…
Kriging is an established methodology for predicting spatial data in geostatistics. Current kriging techniques can handle linear dependencies on spatially referenced covariates. Although splines have shown promise in capturing nonlinear…
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,…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
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…
We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each…
Model averaging, as an appealing ensemble technique, strategically integrates all valuable information from candidate models to construct fast and accurate prediction. Despite of having been widely practiced in many fields such as…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
This paper addresses the asymptotic performance of popular spatial regression estimators of the linear effect of an exposure on an outcome under ``spatial confounding" -- the presence of an unmeasured spatially-structured variable…
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing…
Optimal linear prediction (aka. kriging) of a random field $\{Z(x)\}_{x\in\mathcal{X}}$ indexed by a compact metric space $(\mathcal{X},d_{\mathcal{X}})$ can be obtained if the mean value function $m\colon\mathcal{X}\to\mathbb{R}$ and the…