Prediction intervals with a Dirichlet‐process prior distribution

Let X 1 , …,X n , and Y 1 , … Y n be consecutive samples from a distribution function F which itself is randomly chosen according to the Ferguson (1973) Dirichlet‐process prior distribution on the space of distribution functions. Typically, prediction intervals employ the observations X 1 ,…, X n in the first sample in order to predict a specified function of the future sample Y 1 , …, Y n . Here one‐ and two‐sided prediction intervals for at least q of N future observations are developed for the situation in which, in addition to the previous sample, there is prior information available. The information is specified via the parameter α of the Dirichlet process prior distribution.