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We introduce a novel approach called the Bayesian Jackknife empirical likelihood method for analyzing survey data obtained from various unequal probability sampling designs. This method is particularly applicable to parameters described by…

Methodology · Statistics 2023-09-14 Mengdong Shang , Xia Chen

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

Statistics Theory · Mathematics 2025-08-04 Chang Liu , Ryan Martin , Weining Shen

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

Statistics Theory · Mathematics 2013-12-09 Sergios Agapiou , Andrew M. Stuart , Yuan-Xiang Zhang

This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…

Computation · Statistics 2022-11-01 Kody J. H. Law , Vitaly Zankin

The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…

Statistics Theory · Mathematics 2024-12-10 Ryan Martin , Jonathan P. Williams

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Statistics Theory · Mathematics 2015-10-15 Ismaël Castillo , Johannes Schmidt-Hieber , Aad van der Vaart

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

Methodology · Statistics 2015-09-29 Tiep Mai , Simon Wilson

Inference and estimation are fundamental in statistics, system identification, and machine learning. When prior knowledge about the system is available, Bayesian analysis provides a natural framework for encoding it through a prior…

Systems and Control · Electrical Eng. & Systems 2025-08-29 Yibo Shi , Braghadeesh Lakshminarayanan , Cristian R. Rojas

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

Statistics Theory · Mathematics 2009-08-26 A. W. van der Vaart , J. H. van Zanten

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…

In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…

Methodology · Statistics 2023-06-27 Banoth Veeranna

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…

Machine Learning · Statistics 2024-09-04 The Tien Mai

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

Methodology · Statistics 2017-09-12 Snigdha Panigrahi , Jonathan Taylor

For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular,…

Statistics Theory · Mathematics 2014-10-31 Ryan Martin , Stephen G. Walker

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

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Machine Learning · Statistics 2013-03-26 Rajarshi Guhaniyogi , David B. Dunson

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…

Statistics Theory · Mathematics 2023-08-29 Babak Maboudi Afkham , Kim Knudsen , Aksel Kaastrup Rasmussen , Tanja Tarvainen

This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual…

Methodology · Statistics 2021-01-08 Matthew Reimherr , Xiao-Li Meng , Dan L. Nicolae

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

Statistics Theory · Mathematics 2022-11-29 Ryan Martin

This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…

Artificial Intelligence · Computer Science 2013-01-07 Phan H. Giang , Prakash P. Shenoy