  This paper reviews two main types of prediction interval methods under a
parametric framework. First, we describe methods based on an (approximate)
pivotal quantity. Examples include the plug-in, pivotal, and calibration
methods. Then we describe methods based on a predictive distribution (sometimes
derived based on the likelihood). Examples include Bayesian, fiducial, and
direct-bootstrap methods. Several examples involving continuous distributions
along with simulation studies to evaluate coverage probability properties are
provided. We provide specific connections among different prediction interval
methods for the (log-)location-scale family of distributions. This paper also
discusses general prediction interval methods for discrete data, using the
binomial and Poisson distributions as examples. We also overview methods for
dependent data, with application to time series, spatial data, and Markov
random fields, for example.
