  This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a
model for sequentially observed count tensors that encodes a strong inductive
bias toward sparsity and burstiness. The PRGDS is based on a new motif in
Bayesian latent variable modeling, an alternating chain of discrete Poisson and
continuous gamma latent states that is analytically convenient and
computationally tractable. This motif yields closed-form complete conditionals
for all variables by way of the Bessel distribution and a novel discrete
distribution that we call the shifted confluent hypergeometric distribution. We
draw connections to closely related models and compare the PRGDS to these
models in studies of real-world count data sets of text, international events,
and neural spike trains. We find that a sparse variant of the PRGDS, which
allows the continuous gamma latent states to take values of exactly zero, often
obtains better predictive performance than other models and is uniquely capable
of inferring latent structures that are highly localized in time.
