  We develop constructions for exchangeable sequences of point processes that
are rendered conditionally-i.i.d. negative binomial processes by a (possibly
unknown) random measure called the base measure. Negative binomial processes
are useful in Bayesian nonparametrics as models for random multisets, and in
applications we are often interested in cases when the base measure itself is
difficult to construct (for example when it has countably infinite support).
While a finitary construction for an important case (corresponding to a beta
process base measure) has appeared in the literature, our constructions
generalize to any random base measure, requiring only an exchangeable sequence
of Bernoulli processes rendered conditionally-i.i.d. by the same underlying
random base measure. Because finitary constructions for such Bernoulli
processes are known for several different classes of random base
measures--including generalizations of the beta process and hierarchies
thereof--our results immediately provide constructions for negative binomial
processes with a random base measure from any member of these classes.
