  Healthcare data from patient or population cohorts are often characterized by
sparsity, high missingness and relatively small sample sizes. In addition,
being able to quantify uncertainty is often important in a medical context. To
address these analytical requirements we propose a deep generative Bayesian
model for multinomial count data. We develop a collapsed Gibbs sampling
procedure that takes advantage of a series of augmentation relations, inspired
by the Zhou$\unicode{x2013}$Cong$\unicode{x2013}$Chen model. We visualise the
model's ability to identify coherent substructures in the data using a dataset
of handwritten digits. We then apply it to a large experimental dataset of DNA
mutations in cancer and show that we can identify biologically meaningful
clusters of mutational signatures in a fully data-driven way.
