Approximating Distributions of Random Functionals of Ferguson-Dirichlet Priors. Muliere, P. & Tardella, L. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 26(2):283-297, [Statistical Society of Canada, Wiley], 1998. ![Approximating Distributions of Random Functionals of Ferguson-Dirichlet Priors [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex We explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows us to set in advance the closeness to the distributions of interest. The distribution of the stopping rule is derived, and the practicability of the simulating procedure is discussed. Sufficient conditions for convergence of random functionals are provided. The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting. /// Nous nous proposons d'explorer la possibilité d'approximer une loi de probabilité a priori ayant une distribution de Ferguson-Dirichlet, aussi que les fonctionelles aléatoires de celui-là. La procédure que nous proposons est fondée sur la définition constructive du processus de Ferguson-Dirichlet contenue en Sethuraman (1994) avec l'introduction d'un temp d'arr\^et alèatoire. Ceci permet de choisir a l'avance une limite supérieure pour la distance entre l'approximation et la distribution que nous interest. Nous derivons la distribution du temp d'arr\^et aussi que des conditions suffisantes pour la convergence des fonctionelles alèatoires.
@article{10.2307/3315511,
Abstract = {We explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows us to set in advance the closeness to the distributions of interest. The distribution of the stopping rule is derived, and the practicability of the simulating procedure is discussed. Sufficient conditions for convergence of random functionals are provided. The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting. /// Nous nous proposons d'explorer la possibilit{\'e} d'approximer une loi de probabilit{\'e} a priori ayant une distribution de Ferguson-Dirichlet, aussi que les fonctionelles al{\'e}atoires de celui-l{\`a}. La proc{\'e}dure que nous proposons est fond{\'e}e sur la d{\'e}finition constructive du processus de Ferguson-Dirichlet contenue en Sethuraman (1994) avec l'introduction d'un temp d'arr{\^e}t al{\`e}atoire. Ceci permet de choisir a l'avance une limite sup{\'e}rieure pour la distance entre l'approximation et la distribution que nous interest. Nous derivons la distribution du temp d'arr{\^e}t aussi que des conditions suffisantes pour la convergence des fonctionelles al{\`e}atoires.},
Author = {Pietro Muliere and Luca Tardella},
Date-Added = {2017-10-04 20:19:32 +0000},
Date-Modified = {2017-10-04 20:19:32 +0000},
Issn = {03195724},
Journal = {The Canadian Journal of Statistics / La Revue Canadienne de Statistique},
Number = {2},
Pages = {283-297},
Publisher = {[Statistical Society of Canada, Wiley]},
Title = {Approximating Distributions of Random Functionals of Ferguson-Dirichlet Priors},
Url = {http://www.jstor.org/stable/3315511},
Volume = {26},
Year = {1998},
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The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting. /// Nous nous proposons d'explorer la possibilité d'approximer une loi de probabilité a priori ayant une distribution de Ferguson-Dirichlet, aussi que les fonctionelles aléatoires de celui-là. La procédure que nous proposons est fondée sur la définition constructive du processus de Ferguson-Dirichlet contenue en Sethuraman (1994) avec l'introduction d'un temp d'arr\\^et alèatoire. Ceci permet de choisir a l'avance une limite supérieure pour la distance entre l'approximation et la distribution que nous interest. 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