相关论文: Coverage Properties of Empirical Bayes Intervals

A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…

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…

Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved…

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

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…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

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…

In this paper, I apply the decision theory and empirical Bayesian approach to construct confidence intervals for selected populations when true parameters follow a mixture prior distribution. A loss function with two tuning parameters $k_1$…

Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear…

Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…

In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to…

This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…

Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…

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 this note we consider coverage of confidence intervals calculated with and without systematic uncertainties. These calculations follow the prescription originally proposed by Cousins & Highland but here extended to account for different…

We provide the asymptotic distribution of the major indexes used in the statistical literature to quantify disparate treatment in machine learning. We aim at promoting the use of confidence intervals when testing the so-called group…

Empirical Bayes inference is based on estimation of the parameters of an a priori distribution from the observed data. The estimation technique of the parameters of the prior, called hyperparameters, is based on the marginal distribution…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…