  A beta-negative binomial (BNB) process is proposed, leading to a
beta-gamma-Poisson process, which may be viewed as a "multi-scoop"
generalization of the beta-Bernoulli process. The BNB process is augmented into
a beta-gamma-gamma-Poisson hierarchical structure, and applied as a
nonparametric Bayesian prior for an infinite Poisson factor analysis model. A
finite approximation for the beta process Levy random measure is constructed
for convenient implementation. Efficient MCMC computations are performed with
data augmentation and marginalization techniques. Encouraging results are shown
on document count matrix factorization.
