Penalized regression methods, such as L 1 regularization, are routinely used in high-
dimensional applications, and there is a rich literature on optimality properties under sparsity …

The goal of this paper is to contrast and survey the major advances in two of the most
commonly used high-dimensional techniques, namely, the Lasso and horseshoe …

We propose a Bayesian approach to regression with a scalar response on vector and tensor
covariates. Vectorization of the tensor prior to analysis fails to exploit the structure, often …

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 …

In this paper, we establish some optimality properties of the multiple testing rule induced by
the horseshoe estimator due to Carvalho, Polson, and Scott (2010, 2009) from a Bayesian …

This article develops a Bayesian partitioning prior model from spanning trees of a graph, by
first assigning priors on spanning trees, and then the number and the positions of removed …

A comprehensive methodology for inference in vector autoregressions (VARs) using sign
and other structural restrictions is developed. The reduced-form VAR disturbances are …

Prior distributions for high-dimensional linear regression require specifying a joint
distribution for the unobserved regression coefficients, which is inherently difficult. We …

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies
among multiple time series. They have been widely used in macroeconomics and financial …

It has become routine to collect data that are structured as multiway arrays (tensors). There
is an enormous literature on low rank and sparse matrix factorizations, but limited …