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Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone…

Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and…

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…

Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

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…

The recovery of sparse generative models from few noisy measurements is an important and challenging problem. Many deterministic algorithms rely on some form of $\ell_1$-$\ell_2$ minimization to combine the computational convenience of the…

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Projections of future climate change rely heavily on climate models, and combining climate models through a multi-model ensemble is both more accurate than a single climate model and valuable for uncertainty quantification. However,…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…

We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…