Related papers: Confidence Intervals for Nonparametric Empirical B…

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…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach, that treats the…

We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which…

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…

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…

In Neyman's original formulation, a 1-alpha confidence interval procedure is justified by its long-run coverage properties, and a single realized interval is to be described only by the slogan that it either covers the parameter or it does…

We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest…

It is well known that the asymptotic variance of sample quantiles can be reduced under heterogeneity relative to the i.i.d. setting. However, asymptotically correct confidence intervals for quantiles are not yet available. We propose a…

Population attributable risk (PAR) is used in epidemiology to predict the impact of removing a risk factor from the population. Until recently, no standard approach for calculating confidence intervals or the variance for PAR was available…

Consider a Bayesian situation in which we observe $Y \sim p_{\theta}$, where $\theta \in \Theta$, and we have a family $\{ \nu_h, \, h \in \mathcal{H} \}$ of potential prior distributions on $\Theta$. Let $g$ be a real-valued function of…

We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…

We propose using a Bayes procedure with uniform improper prior to determine credible belts for the mean of a Poisson distribution in the presence of background and for the continuous problem of measuring a non-negative quantity $\theta$…

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,…