Related papers: Empirical priors for prediction in sparse high-dim…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

We study asymptotic frequentist coverage and approximately Gaussian properties of Bayes posterior credible sets in nonlinear inverse problems when a Gaussian prior is placed on the parameter of the PDE. The aim is to ensure valid…

In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

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…

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…

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

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…

We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined,…

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Empirical Bayes is a versatile approach to `learn from a lot' in two ways: first, from a large number of variables and second, from a potentially large amount of prior information, e.g. stored in public repositories. We review applications…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…