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Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture…

Statistics Theory · Mathematics 2021-01-13 Kyoungjae Lee , Seongil Jo , Jaeyong Lee

Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…

Econometrics · Economics 2020-08-27 Niko Hauzenberger , Florian Huber , Luca Onorante

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…

Statistics Theory · Mathematics 2015-07-27 Prasenjit Ghosh , Arijit Chakrabarti

We investigate estimation of a normal mean matrix under the matrix quadratic loss. Improved estimation under the matrix quadratic loss implies improved estimation of any linear combination of the columns. First, an unbiased estimate of risk…

Statistics Theory · Mathematics 2021-04-05 Takeru Matsuda , William E. Strawderman

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Econometrics · Economics 2021-12-23 Dimitris Korobilis , Kenichi Shimizu

This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many…

Methodology · Statistics 2014-08-05 P. Richard Hahn , Hedibert Lopes

Vector autogressions (VARs) are widely applied when it comes to modeling and forecasting macroeconomic variables. In high dimensions, however, they are prone to overfitting. Bayesian methods, more concretely shrinkage priors, have shown to…

Econometrics · Economics 2025-02-27 Luis Gruber , Gregor Kastner

In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…

Statistics Theory · Mathematics 2020-01-16 Ruoyang Zhang , Malay Ghosh

This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…

Methodology · Statistics 2017-02-20 Xianyang Zhang , Anirban Bhattacharya

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,…

Methodology · Statistics 2020-11-12 Alex Rodrigo dos Santos Sousa , Nancy Lopes Garcia , Branislav Vidakovic

Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…

Machine Learning · Statistics 2026-05-05 Mame Diarra Toure , David A. Stephens

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…

Statistics Theory · Mathematics 2017-11-21 Tavis Abrahamsen , James P. Hobert

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are…

Statistics Theory · Mathematics 2023-11-06 Yasuyuki Hamura

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…

Statistics Theory · Mathematics 2014-06-03 Debdeep Pati , Anirban Bhattacharya , Natesh S. Pillai , David Dunson

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…

Methodology · Statistics 2025-12-02 Debamita Kundu , Riten Mitra , Jeremy T. Gaskins

This paper proposes a class of asymmetric priors to perform Bayesian wavelet shrinkage in the standard nonparametric regression model with Gaussian error. The priors are composed by mixtures of a point mass function at zero and one of the…

Methodology · Statistics 2024-10-03 Alex Rodrigo dos Santos Sousa

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…

Statistics Theory · Mathematics 2016-05-19 Anirban Bhattacharya , David B. Dunson , Debdeep Pati , Natesh S. Pillai

We consider sparse Bayesian estimation in the classical multivariate linear regression model with $p$ regressors and $q$ response variables. In univariate Bayesian linear regression with a single response $y$, shrinkage priors which can be…

Methodology · Statistics 2018-05-21 Ray Bai , Malay Ghosh

We consider the problem of estimating a low-rank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased…

Statistics Theory · Mathematics 2017-10-03 Jérémie Bigot , Charles Deledalle , Delphine Féral

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…

Statistics Theory · Mathematics 2012-12-27 Anirban Bhattacharya , Debdeep Pati , Natesh S. Pillai , David B. Dunson