- Volume 22, Number 4 (2016), 2301-2324.
The combinatorial structure of beta negative binomial processes
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.
Bernoulli, Volume 22, Number 4 (2016), 2301-2324.
Received: June 2014
Revised: March 2015
First available in Project Euclid: 3 May 2016
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Heaukulani, Creighton; Roy, Daniel M. The combinatorial structure of beta negative binomial processes. Bernoulli 22 (2016), no. 4, 2301--2324. doi:10.3150/15-BEJ729. https://projecteuclid.org/euclid.bj/1462297682