Related papers: Log-Scale Shrinkage Priors and Adaptive Bayesian G…
We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we demonstrate the horseshoe priors, originally…
The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but has previously suffered from two problems. First, there has been no systematic way of specifying a prior for the global shrinkage…
High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…
We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a…
Researchers and managers model ecological communities to infer the biotic and abiotic variables that shape species' ranges, habitat use, and co-occurrence which, in turn, are used to support management decisions and test ecological…
Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture…
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.…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to predictors with grouping structures. Of particular interest in…
Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping…
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 assumptions. In the Bayesian paradigm, sparsity is…
We introduce GRASP, a simple Bayesian framework for regression with grouped predictors, built on the normal beta prime (NBP) prior. The NBP prior is an adaptive generalization of the horseshoe prior with tunable hyperparameters that control…
Suppose we have data generated according to a multivariate normal distribution with a fixed unknown mean vector that is sparse in the sense of being nearly black. Optimality of Bayes estimates and posterior concentration properties in terms…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
Currently several Bayesian approaches are available to estimate large sparse precision matrices, including Bayesian graphical Lasso (Wang, 2012), Bayesian structure learning (Banerjee and Ghosal, 2015), and graphical horseshoe (Li et al.,…
The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. The idea is to search for the sparsest solution within the joint posterior credible regions. Although the approach was…
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The…
The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous…