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.
"The combinatorial structure of beta negative binomial processes." Bernoulli 22 (4) 2301 - 2324, November 2016. https://doi.org/10.3150/15-BEJ729