Confidence intervals for the normal mean utilizing prior information

TL;DR

This paper investigates how to incorporate uncertain prior information that the mean is zero into frequentist confidence intervals for the normal mean, aiming to improve their efficiency.

Contribution

It develops methods to adapt confidence intervals for the normal mean using uncertain prior information, balancing prior knowledge with data.

Findings

Improved confidence intervals that leverage prior information

Quantitative assessment of the benefit of using prior info

Guidelines for applying these methods in practice

Abstract

Consider X_1,X_2,...,X_n that are independent and identically N(mu,sigma^2) distributed. Suppose that we have uncertain prior information that mu = 0. We answer the question: to what extent can a frequentist 1-alpha confidence interval for mu utilize this prior information?