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We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or…

Statistics Theory · Mathematics 2007-06-13 Fumiyasu Komaki

We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…

Statistics Theory · Mathematics 2022-08-16 Gianluca Finocchio , Johannes Schmidt-Hieber

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…

Statistics Theory · Mathematics 2013-09-10 Abhra Sarkar , Debdeep Pati , Bani K. Mallick , Raymond J. Carroll

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

Statistics Theory · Mathematics 2020-02-04 Jan van Waaij

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

Methodology · Statistics 2021-05-12 Rajarshi Guhaniyogi , Aaron Scheffler

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

Methodology · Statistics 2022-07-04 Chang Liu , Yue Yang , Howard Bondell , Ryan Martin

Macroeconomists using large datasets often face the choice of working with either a large Vector Autoregression (VAR) or a factor model. In this paper, we develop methods for combining the two using a subspace shrinkage prior. Subspace…

Econometrics · Economics 2021-07-19 Florian Huber , Gary Koop

Regularization in fitting regression models has been a highly active topic of research in the past few decades, but most of the existing methods are designed for particular situations, e.g. for the case of a sparse coefficient vector. We…

Methodology · Statistics 2025-05-15 Asaf Weinstein , Jonas Wallin , Daniel Yekutieli , Małgorzata Bogdan

We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…

Methodology · Statistics 2011-10-07 Hao Wang , Natesh S. Pillai

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

Methodology · Statistics 2025-02-04 Aihua Li , Surya T. Tokdar , Jason Xu

We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the…

Statistics Theory · Mathematics 2007-06-13 Kei Kobayashi , Fumiyasu Komaki

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…

Methodology · Statistics 2021-07-13 Niloy Biswas , Anirban Bhattacharya , Pierre E. Jacob , James E. Johndrow

Prediction of a vector of ordered parameters or part of it arises naturally in the context of Small Area Estimation (SAE). For example, one may want to estimate the parameters associated with the top ten areas, the best or worst area, or a…

Methodology · Statistics 2012-10-30 Yaakov Malinovsky , Yosef Rinott

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

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Machine Learning · Statistics 2022-09-28 Felix Schneider , Iason Papaioannou , Gerhard Müller

Stochastic delays in feedback lead to unstable sequential learning using multi-armed bandits. Recently, empirical Bayesian shrinkage has been shown to improve reward estimation in bandit learning. Here, we propose a novel adaptation to…

Machine Learning · Computer Science 2021-06-23 Srivas Chennu , Jamie Martin , Puli Liyanagama , Phil Mohr

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

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

Methodology · Statistics 2015-07-30 Elías Moreno , Javier Girón , George Casella

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

Methodology · Statistics 2022-12-08 Michiko Okudo , Fumiyasu Komaki