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Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…

In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data…

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…

Subspace-valued functions arise in a wide range of problems, including parametric reduced order modeling (PROM). In PROM, each parameter point can be associated with a subspace, which is used for Petrov-Galerkin projections of large system…

The flexibility of the Bayesian approach to account for covariates with measurement error is combined with semiparametric regression models for a class of continuous, discrete and mixed univariate response distributions with potentially all…

This paper proposes a heterogenous density fusion approach to scalable multisensor multitarget tracking where the inter-connected sensors run different types of random finite set (RFS) filters according to their respective capacity and…

Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct…

Arsenic (As) and other toxic elements contamination of groundwater in Bangladesh poses a major threat to millions of people on a daily basis. Understanding complex relationships between arsenic and other elements can provide useful insights…

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…

Unmeasured confounding bias threatens the validity of observational studies. While sensitivity analyses and study designs have been proposed to address this issue, they often overlook the growing availability of auxiliary data. Using…

Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a…

Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the…

Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data,…

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…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

Modeling the relationship between vehicle speed and density on the road is a fundamental problem in traffic flow theory. Recent research found that using the least-squares (LS) method to calibrate single-regime speed-density models is…

Extreme floods cause casualties, and widespread damage to property and vital civil infrastructure. We here propose a Bayesian approach for predicting extreme floods using the generalized extreme-value (GEV) distribution within gauged and…

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…