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Prediction intervals with a Dirichlet‐process prior distribution
Author(s) -
Campbell Gregory,
Hollander Myles
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314902
Subject(s) - dirichlet distribution , mathematics , dirichlet process , distribution (mathematics) , statistics , sample (material) , sample space , distribution function , function (biology) , concentration parameter , order statistic , combinatorics , mathematical analysis , physics , thermodynamics , bayesian probability , evolutionary biology , biology , boundary value problem
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.