Methods to Compute Prediction Intervals: A Review and New Results

Abstract

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).