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Gaussian processes are ubiquitous as the primary tool for modeling spatial data. However, the Gaussian process is limited by its $\mathcal{O}(n^3)$ cost, making direct parameter fitting algorithms infeasible for the scale of modern data…
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…
Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…
We consider alternate formulations of recently proposed hierarchical Nearest Neighbor Gaussian Process (NNGP) models (Datta et al., 2016a) for improved convergence, faster computing time, and more robust and reproducible Bayesian inference.…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…
Gaussian Processes (GP) is a staple in the toolkit of a spatial statistician. Well-documented computing roadblocks in the analysis of large geospatial datasets using Gaussian Processes have now been successfully mitigated via several recent…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Obtaining accurate water level predictions are essential for water resource management and implementing flood mitigation strategies. Several data-driven models can be found in the literature. However, there has been limited research with…
Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…
The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix.…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…