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The next generation of Department of Energy supercomputers will be capable of exascale computation. For these machines, far more computation will be possible than that which can be saved to disk. As a result, users will be unable to rely on…
Sustainable management of groundwater resources under changing climatic conditions require an application of reliable and accurate predictions of groundwater levels. Mechanistic multi-scale, multi-physics simulation models are often too…
Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from…
Temporal variations of apparent magnitude, called light curves, are observational statistics of interest captured by telescopes over long periods of time. Light curves afford the exploration of Space Domain Awareness (SDA) objectives such…
Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…
In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…
We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
Water temperature can vary substantially even across short distances within the same sub-watershed. Accurate prediction of stream water temperature at fine spatial resolutions (i.e., fine scales, $\leq$ 1 km) enables precise interventions…
Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
Multivariate Gaussian processes (GPs) offer a powerful probabilistic framework to represent complex interdependent phenomena. They pose, however, significant computational challenges in high-dimensional settings, which frequently arise in…
Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…
Inter-domain Gaussian processes (GPs) allow for high flexibility and low computational cost when performing approximate inference in GP models. They are particularly suitable for modeling data exhibiting global structure but are limited to…
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
Spatial statistics often rely on Gaussian processes (GPs) to capture dependencies across locations. However, their computational cost increases rapidly with the number of locations, potentially needing multiple hours even for moderate…
With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…