  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.
