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We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
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…
Unmeasured spatial confounding complicates exposure effect estimation in environmental health studies. This problem is exacerbated in studies with multiple health outcomes and environmental exposure variables, as the source and magnitude of…
Model calibration or data inversion is one of fundamental tasks in uncertainty quantification. In this work, we study the theoretical properties of the scaled Gaussian stochastic process (S-GaSP), to model the discrepancy between reality…
In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Propensity score (PS) matching to estimate causal effects of exposure is biased when unmeasured spatial confounding exists. Some exposures are continuous yet dependent on a binary variable (e.g., level of a contaminant (continuous) within a…
We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…
Scientists are often interested in estimating an association between a covariate and a binary- or count-valued response. For instance, public health officials are interested in how much disease presence (a binary response per individual)…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
We extend field-level inference to jointly constrain the cosmological parameters $\{A,\omega_{\rm cdm},H_0\}$, in both real and redshift space. Our analyses are based on mock data generated using a perturbative forward model, with noise…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study…
Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and…
In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied,…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
This paper proposes a new approach to address the problem of unmeasured confounding in spatial designs. Spatial confounding occurs when some confounding variables are unobserved and not included in the model, leading to distorted…
We present Stochastic Gaussian Splatting (SGS): the first framework for uncertainty estimation using Gaussian Splatting (GS). GS recently advanced the novel-view synthesis field by achieving impressive reconstruction quality at a fraction…
We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…