Related papers: Nonparametric Empirical Bayes Confidence Intervals
The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…
We contribute to bridging the gap between large- and finite-sample inference by studying confidence sets (CSs) that are both non-asymptotically valid and asymptotically exact uniformly (NAVAE) over semi-parametric statistical models. NAVAE…
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…
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…
Real-world applications often require improved models by leveraging a range of cheap incidental supervision signals. These could include partial labels, noisy labels, knowledge-based constraints, and cross-domain or cross-task annotations…
This work considers the problem of calculating an interval-valued state estimate for a nonlinear system subject to bounded inputs and measurement errors. Such state estimators are often called interval observers. Interval observers can be…
In this article, we derive the joint asymptotic distribution of empirical best linear unbiased predictors (EBLUPs) for individual and cell-level random effects in a crossed mixed effect model. Under mild conditions (which include moment…
We design a debiased parametric bootstrap framework for statistical inference from differentially private data. Existing usage of the parametric bootstrap on privatized data ignored or avoided handling possible biases introduced by the…
Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…
The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It…
Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented. Introducing the conditional probability satisfying the…
Empirical Bayes (EB) is a popular framework for large-scale inference that aims to find data-driven estimators to compete with the Bayesian oracle that knows the true prior. Two principled approaches to EB estimation have emerged over the…
Biomarkers are often measured in bulk to diagnose patients, monitor patient conditions, and research novel drug pathways. The measurement of these biomarkers often suffers from detection limits that result in missing and untrustworthy…
PAC-Bayesian analysis is a frequentist framework for incorporating prior knowledge into learning. It was inspired by Bayesian learning, which allows sequential data processing and naturally turns posteriors from one processing step into…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We combine two important ideas in the analysis of large-scale genomics experiments (e.g. experiments that aim to identify genes that are differentially expressed between two conditions). The first is use of Empirical Bayes (EB) methods to…
The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…