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We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of…
In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…
Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…
In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
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,…
Empirical Bayes methods offer valuable tools for a large class of compound decision problems. In this tutorial we describe some basic principles of the empirical Bayes paradigm stressing their frequentist interpretation. Emphasis is placed…
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…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…