The Annals of Statistics

Theory and numerical analysis for exact distributions of functionals of a Dirichlet process

Eugenio Regazzini, Alessandra Guglielmi, and Giulia Di Nunno

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Abstract

The distribution of a mean or, more generally, of a vector of means of a Dirichlet process is considered. Some characterizing aspects of this paper are: (i) a review of a few basic results, providing new formulations free from many of the extra assumptions considered to date in the literature, and giving essentially new, simpler and more direct proofs; (ii) new numerical evaluations, with any prescribed error of approximation, of the distribution at issue; (iii) a new form for the law of a vector of means. Moreover, as applications of these results, we give: (iv) the sharpest condition sufficient for the distribution of a mean to be symmetric; (v) forms for the probability distribution of the variance of the Dirichlet random measure; (vi) some hints for determining the finite-dimensional distributions of a random function connected with Bayesian methods for queuing models.

Article information

Source
Ann. Statist., Volume 30, Number 5 (2002), 1376-1411.

Dates
First available in Project Euclid: 28 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1035844980

Digital Object Identifier
doi:10.1214/aos/1035844980

Mathematical Reviews number (MathSciNet)
MR1936323

Zentralblatt MATH identifier
1018.62011

Subjects
Primary: 62F15: Bayesian inference
Secondary: 60E15: Inequalities; stochastic orderings 62E17: Approximations to distributions (nonasymptotic)

Keywords
Dirichlet process distribution of (a vector of) linear functionals numerical approximation of the exact distribution

Citation

Regazzini, Eugenio; Guglielmi, Alessandra; Di Nunno, Giulia. Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30 (2002), no. 5, 1376--1411. doi:10.1214/aos/1035844980. https://projecteuclid.org/euclid.aos/1035844980


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  • VIA FERRATA, 1 27100 PAVIA ITALY E-MAIL: eugenio@dimat.unipv.it giulia@dimat.unipv.it A. GUGLIELMI ISTITUTO PER LE APPLICAZIONI DELLA MATEMATICA E DELL'INFORMATICA CONSIGLIO NAZIONALE DELLE RICERCHE
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