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Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…

There is a wide variety of models in which the dimension of the parameter space is unknown. For example, in factor analysis the number of latent factors is typically not known and has to be inferred from the observed data. Although…

In recent years there has been an increasing interest in the use of relational event models for dynamic social network analysis. The basis of these models is the concept of an "event", defined as a triplet of time, sender, and receiver of…

We introduce BLAST, Bayesian Linear regression with Adaptive Shrinkage for Transfer, a Bayesian multi-source transfer learning framework for high-dimensional linear regression. The proposed analytical framework leverages global-local…

Demographic and health indicators may exhibit short or large short-term shocks; for example, armed conflicts, epidemics, or famines may cause shocks in period measures of life expectancy. Statistical models for estimating historical trends…

We discovered that past changes in the market correlation structure are significantly related with future changes in the market volatility. By using correlation-based information filtering networks we device a new tool for forecasting the…

We study the construction and rebalancing of sparse index-tracking portfolios from an operational research perspective, with explicit emphasis on uncertainty quantification and implementability. The decision variables are portfolio weights…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…

Forecasting inflation in small open economies is difficult because limited time series and strong external exposures create an imbalance between few observations and many potential predictors. We study this challenge using Thailand as a…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…

Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…