Open Access
November 2016 The combinatorial structure of beta negative binomial processes
Creighton Heaukulani, Daniel M. Roy
Bernoulli 22(4): 2301-2324 (November 2016). DOI: 10.3150/15-BEJ729


We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from conditionally-i.i.d. sequences of Bernoulli processes with a common beta process base measure, in which case the combinatorial structure is described by the Indian buffet process. Our results give a count analogue of the Indian buffet process, which we call a negative binomial Indian buffet process. As an intermediate step toward this goal, we provide a construction for the beta negative binomial process that avoids a representation of the underlying beta process base measure. We describe the key Markov kernels needed to use a NB-IBP representation in a Markov Chain Monte Carlo algorithm targeting a posterior distribution.


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Creighton Heaukulani. Daniel M. Roy. "The combinatorial structure of beta negative binomial processes." Bernoulli 22 (4) 2301 - 2324, November 2016.


Received: 1 June 2014; Revised: 1 March 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1358.60069
MathSciNet: MR3498030
Digital Object Identifier: 10.3150/15-BEJ729

Keywords: Bayesian nonparametrics , Indian buffet process , latent feature models , multisets

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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