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Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG…

We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…

Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…

This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Berger et al. (2001) and Ren et al. (2012) derived noninformative priors for Gaussian process models of spatially correlated data using the reference prior approach (Berger, Bernardo, 1991). The priors have good statistical properties and…

In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…