Related papers: Stochastic Local Interaction Model: Geostatistics …

Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the…

The application of geostatistical and machine learning methods based on Gaussian processes to big space-time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally…

Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…

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…

Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the…

In this article, we review and compare a number of methods of spatial prediction. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition…

Spatial prediction in an arbitrary location, based on a spatial set of observations, is usually performed by Kriging, being the best linear unbiased predictor (BLUP) in a least-square sense. In order to predict a continuous surface over a…

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…

Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and…

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers…

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…

Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

It is well-known from the work of Sch\"onbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The…

Spatial statistical modeling and prediction involve generating and manipulating an n*n symmetric positive definite covariance matrix, where n denotes the number of spatial locations. However, when n is large, processing this covariance…

Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present 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…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

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…

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…