Related papers: Correcting spatial Gaussian process parameter 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…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically…
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…
Preferential sampling provides a formal modeling specification to capture the effect of bias in a set of sampling locations on inference when a geostatistical model is used to explain observed responses at the sampled locations. In…
The proliferation of unmanned vehicles offers many opportunities for solving environmental sampling tasks with applications in resource monitoring and precision agriculture. Informative path planning (IPP) includes a family of methods which…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
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…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…
Studies investigating the causal effects of spatially varying exposures on outcomes often rely on observational and spatially indexed data. A prevalent challenge is unmeasured spatial confounding, where an unobserved spatially varying…
The problem of choosing spatial sampling designs for investigating unobserved spatial phenomenon S arises in many contexts, for example in identifying households to select for a prevalence survey to study disease burden and heterogeneity in…
In our previous work, we designed a systematic policy to prioritize sampling locations to lead significant accuracy improvement in spatial interpolation by using the prediction uncertainty of Gaussian Process Regression (GPR) as "attraction…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
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 spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…
Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities…
An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…
Treeging combines the flexible mean structure of regression trees with the covariance-based prediction strategy of kriging into the base learner of an ensemble prediction algorithm. In so doing, it combines the strengths of the two primary…
In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical data. Among these, maximum likelihood estimators have nice features when we deal with a Gaussian model. However…