The purpose of this paper is to review both classic and modern methods for constructing prediction intervals. We focus, primarily, on model-based non-Bayesian methods for the prediction of a scalar random variable, but we also include Bayesian methods with objective prior distributions. Our review of non-Bayesian methods follows two lines: general methods based on (approximate) pivotal quantities and methods based on non-Bayesian predictive distributions. The connection between these two types of methods is described for distributions in the (log-)location-scale family. We also discuss extending the general prediction methods to data with complicated dependence structures as well as some nonparametric prediction methods (e.g., conformal prediction).
The research was partially supported by NSF DMS-2015390.
We would like to thank Professor Jan Hannig for providing a copy of his MATLAB code for computing the Gamma fiducial distribution and Professor Luis A. Escobar for helpful guidance on the use of the pivotal methods for discrete distributions. We would also like to thank the editor, associate editor, and referees for their constructive and helpful comments.
Qinglong Tian. Daniel J. Nordman. William Q. Meeker. "Methods to Compute Prediction Intervals: A Review and New Results." Statist. Sci. 37 (4) 580 - 597, November 2022. https://doi.org/10.1214/21-STS842