We study the problem of estimating finite sample confidence intervals of the mean of a
normal population under the constraint of differential privacy. We consider both the known …

This paper addresses the issue of optimal inference for parameters that are partially
identified in models with moment inequalities. There currently exists a variety of inferential …

Statistical decision rules map data into actions. Point estimators, inference procedures, and
forecasting methods can be viewed as statistical decision rules. However, other types of …

In quantum tomography, a quantum state or process is estimated from the results of
measurements on many identically prepared systems. Tomography can never identify the …

Adaptive confidence intervals for regression functions are constructed under shape
constraints of monotonicity and convexity. A natural benchmark is established for the …

Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-
level spectrum from smeared detector-level data. For computational and practical reasons …

Commonly used interval procedures for multigroup data attain their nominal coverage rates
across a population of groups on average, but their actual coverage rate for a given group …

There are deep and important philosophical differences between Bayesian and frequentist
approaches to quantifying uncertainty. However, some practitioners choose between these …

Inverse problems seek to learn about the world from indirect, noisy data. They can be cast as
statistical estimation problems and studied using statistical decision theory, a framework that …

In recent years, we have seen a diverse range of crises and controversies concerning food
safety, animal health and environmental risks including foot and mouth disease, dioxins in …