Related papers: Confidence Intervals for Nonparametric Empirical B…

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…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…

A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…

We introduce a new adjusted residual maximum likelihood method (REML) in the context of producing an empirical Bayes (EB) confidence interval for a normal mean, a problem of great interest in different small area applications. Like other…

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…

Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of…

Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in…

The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…

We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from…

In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…

We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…

The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…