Some New Results for Dirichlet Priors

Let p be a random probability measure chosen by a Dirichlet process whose parameter α is a finite measure with support contained in [0, +∞) and suppose that V = ∫ x2p(dx)-[∫ xp(dx)]2 is a (finite) random variable. This paper deals with the distribution of V, which is given in a rather general case....

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Bibliographic Details
Published in:The Annals of statistics 2000-10, Vol.28 (5), p.1390-1413
Main Authors: Cifarelli, Donato Michele, Melilli, Eugenio
Format: Article
Language:English
Subjects:
62E15
62G99
Average linear density
Bayesian Nonparametrics and Prediction
Density
Dirichlet process
Distribution functions
distribution of the variance
Distribution theory
Exact sciences and technology
Hypergeometric functions
Integers
Laplace transformation
Mathematical independent variables
Mathematical moments
Mathematics
Nonparametric inference
Parametric inference
Probabilities
Probability and statistics
Probability distributions
Sciences and techniques of general use
Statistics
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Summary:Let p be a random probability measure chosen by a Dirichlet process whose parameter α is a finite measure with support contained in [0, +∞) and suppose that V = ∫ x2p(dx)-[∫ xp(dx)]2 is a (finite) random variable. This paper deals with the distribution of V, which is given in a rather general case. A simple application to Bayesian bootstrap is also illustrated.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1015957399