Graphical models are powerful tools that are regularly used to investigate complex
dependence structures in high-throughput biomedical datasets. They allow for holistic …

This paper proposes a new approach to sparsity, called the horseshoe estimator, which
arises from a prior based on multivariate-normal scale mixtures. We describe the estimator's …

One important aspect of Bayesian model selection is how to deal with huge model spaces,
since the exhaustive enumeration of all the models entertained is not feasible and …

This paper presents a general, fully Bayesian framework for sparse supervised-learning
problems based on the horseshoe prior. The horseshoe prior is a member of the family of …

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection
priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction …

We provide a review of prior distributions for objective Bayesian analysis. We start by
examining some foundational issues and then organize our exposition into priors for: i) …

Recently, the graphical lasso procedure has become popular in estimating Gaussian
graphical models. In this paper, we introduce a fully Bayesian treatment of graphical lasso …

Decoding complex relationships among large numbers of variables with relatively few
observations is one of the crucial issues in science. One approach to this problem is …

We introduce efficient Markov chain Monte Carlo methods for inference and model
determination in multivariate and matrix-variate Gaussian graphical models. Our framework …

We propose a Bayesian procedure for simultaneous variable and covariance selection
using continuous spike-and-slab priors in multivariate linear regression models where q …