Related papers: Scalable Bayesian shrinkage and uncertainty quanti…

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.…

High-dimensional data, where the number of variables exceeds or is comparable to the sample size, is now pervasive in many scientific applications. In recent years, Bayesian shrinkage models have been developed as effective and…

In the past decade, many Bayesian shrinkage models have been developed for linear regression problems where the number of covariates, $p$, is large. Computing the intractable posterior are often done with three-block Gibbs samplers (3BG),…

When performing Bayesian data analysis using a general linear mixed model, the resulting posterior density is almost always analytically intractable. However, if proper conditionally conjugate priors are used, there is a simple two-block…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…

Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…

The Bayesian probit regression model (Albert and Chib (1993)) is popular and widely used for binary regression. While the improper flat prior for the regression coefficients is an appropriate choice in the absence of any prior information,…

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…

For Bayesian learning, given likelihood function and Gaussian prior, the elliptical slice sampler, introduced by Murray, Adams and MacKay 2010, provides a tool for the construction of a Markov chain for approximate sampling of the…

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the…

Use of continuous shrinkage priors -- with a "spike" near zero and heavy-tails towards infinity -- is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the…

In this study, we present a comprehensive evaluation of the Two-Block Gibbs (2BG) sampler as a robust alternative to the traditional Three-Block Gibbs (3BG) sampler in Bayesian shrinkage models. Through extensive simulation studies, we…