Related papers: Indexing and Partitioning the Spatial Linear Model…

Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets,…

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…

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…

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…

Due to the significant increase in the size of spatial data, it is essential to use distributed parallel processing systems to efficiently analyze spatial data. In this paper, we first study learned spatial data partitioning, which…

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…

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…

We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions,…

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…

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…

This paper presents a hybrid approach to spatial indexing of two dimensional data. It sheds new light on the age old problem by thinking of the traditional algorithms as working with images. Inspiration is drawn from an analogous situation…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

Statistical quality control in semiconductor manufacturing hinges on effective diagnostics of wafer bin maps, wherein a key challenge is to detect how defective chips tend to spatially cluster on a wafer--a problem known as spatial pattern…

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…

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…

Efficient spatial indexing is crucial for processing large-scale spatial data. Traditional spatial indexes, such as STR-Tree and Quad-Tree, organize spatial objects based on coarse approximations, such as their minimum bounding rectangles…

Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index, which replaces or complements traditional index structures with machine learning models, has been actively…

We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which…

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…

Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention…