Open Access
April 2015 Central limit theorems for an Indian buffet model with random weights
Patrizia Berti, Irene Crimaldi, Luca Pratelli, Pietro Rigo
Ann. Appl. Probab. 25(2): 523-547 (April 2015). DOI: 10.1214/14-AAP1002


The three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let $L_{n}$ be the number of dishes experimented by the first $n$ customers, and let $\overline{K}_{n}=(1/n)\sum_{i=1}^{n}K_{i}$ where $K_{i}$ is the number of dishes tried by customer $i$. The asymptotic distributions of $L_{n}$ and $\overline{K}_{n}$, suitably centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., nongeneralized) Indian buffet process.


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Patrizia Berti. Irene Crimaldi. Luca Pratelli. Pietro Rigo. "Central limit theorems for an Indian buffet model with random weights." Ann. Appl. Probab. 25 (2) 523 - 547, April 2015.


Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1314.60015
MathSciNet: MR3313747
Digital Object Identifier: 10.1214/14-AAP1002

Primary: 60B10 , 60F05 , 60G09 , 60G57 , 62F15

Keywords: Bayesian nonparametrics , central limit theorem , conditional identity in distribution , Indian buffet process , random measure , random reinforcement , stable convergence

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.25 • No. 2 • April 2015
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