Interval Estimation

June 10, 2013

This is a review of interval construction methods, both frequentist and Bayesian. The frequentist side covers Neyman’s construction, test inversion, pivoting, asymptotic approximations, the bootstrap, and various techniques for handling nuisance parameters. On the Bayesian side the discussion includes highest posterior density regions, equal-tailed intervals, upper and lower limits, likelihood regions, and lowest posterior loss regions. Many examples are given to illustrate the concepts. The review ends with a discussion of the role of intervals in search procedures in high energy physics.

Published as chapter 4 (pg. 107-151) in “Data Analysis in High Energy Physics: a Practical Guide to Statistical Methods,” edited by Olaf Behnke, Kevin Kröninger, Grégory Schott, and Thomas Schörner-Sadenius, Wiley (2013) (ISBN 978-3-527-41058-3).

A preproduction version of the chapter can be downloaded from here.