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In this article, we investigate certain asymptotic optimality properties of a very broad class of one-group continuous shrinkage priors for simultaneous estimation and testing of a sparse normal mean vector. Asymptotic optimality of Bayes…

Statistics Theory · Mathematics 2015-11-11 Prasenjit Ghosh , Arijit Chakrabarti

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…

Methodology · Statistics 2024-11-04 Yuexi Wang , Nicholas G. Polson

Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…

Methodology · Statistics 2025-02-05 Linda S. L. Tan , Aoxiang Chen

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Methodology · Statistics 2022-10-27 Qinglong Tian , Colin Lewis-Beck , Jarad Niemi , William Meeker

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

This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our…

Methodology · Statistics 2011-09-27 Nicholas G. Polson , James G. Scott

Bayesian fused lasso is one of the sparse Bayesian methods, which shrinks both regression coefficients and their successive differences simultaneously. In this paper, we propose a Bayesian fused lasso modeling via horseshoe prior. By…

Methodology · Statistics 2022-01-21 Yuko Kakikawa , Kaito Shimamura , Shuichi Kawano

We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of…

Statistics Theory · Mathematics 2017-02-14 Stéphanie van der Pas , Botond Szabó , Aad van der Vaart

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,…

Statistics Theory · Mathematics 2022-10-11 Qifan Song , Faming Liang

Small area estimation (SAE) plays a central role in survey statistics and epidemiology, providing reliable estimates for domains with limited sample sizes. The multivariate Fay-Herriot model has been extensively used for this purpose,…

Methodology · Statistics 2026-01-22 Shushi Nishina , Takahiro Onizuka , Shintaro Hashimoto

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Machine Learning · Statistics 2020-01-16 Ali Siahkoohi , Gabrio Rizzuti , Felix J. Herrmann

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…

Methodology · Statistics 2026-05-08 Zihan Zhu , Xueying Tang , Shuang Zhou

This is a companion paper to Yarkoni and Westfall (2017), which describes the Python package Bambi for estimating Bayesian generalized linear mixed models using a simple interface. Here I give the statistical details underlying the default,…

Applications · Statistics 2017-02-14 Jacob Westfall

In recent years, Bayesian statistics methods in neuroscience have been showing important advances. In particular, detection of brain signals for studying the complexity of the brain is an active area of research. Functional magnetic…

Methodology · Statistics 2017-06-06 Jairo Alberto Fuquene Patiño , Brenda Betancourt , João B. M. Pereira

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Statistics Theory · Mathematics 2024-06-03 Veronika Rockova

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

Methodology · Statistics 2019-07-02 Daniel R. Kowal , David S. Matteson , David Ruppert

The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage…

Statistics Theory · Mathematics 2016-08-16 Stéphanie van der Pas , Jean-Bernard Salomond , Johannes Schmidt-Hieber

We propose Bayesian Univariate-Guided Sparse Regression (BUGS), a novel global-local shrinkage framework that incorporates marginal association information directly into the prior through a continuous modulation of shrinkage. Unlike…

Methodology · Statistics 2026-04-27 Priyam Das

The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…

Populations and Evolution · Quantitative Biology 2023-09-12 Amine M. Remita , Golrokh Vitae , Abdoulaye Baniré Diallo

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

Statistics Theory · Mathematics 2021-05-12 Daniel G. Rasines , G. Alastair Young