  The analysis of single-cell RNA sequencing (scRNA-seq) data often involves
fitting a latent variable model to learn a low-dimensional representation for
the cells. Validating such a model poses a major challenge. If we could
sequence the same set of cells twice, we could use one dataset to fit a latent
variable model and the other to validate it. In reality, we cannot sequence the
same set of cells twice. Poisson count splitting was recently proposed as a way
to work backwards from a single observed Poisson data matrix to obtain
independent Poisson training and test matrices that could have arisen from two
independent sequencing experiments conducted on the same set of cells. However,
the Poisson count splitting approach requires that the original data are
exactly Poisson distributed: in the presence of any overdispersion, the
resulting training and test datasets are not independent. In this paper, we
introduce negative binomial count splitting, which extends Poisson count
splitting to the more flexible negative binomial setting. Given an $n \times p$
dataset from a negative binomial distribution, we use Dirichlet-multinomial
sampling to create two or more independent $n \times p$ negative binomial
datasets. We show that this procedure outperforms Poisson count splitting in
simulation, and apply it to validate clusters of kidney cells from a human
fetal cell atlas.
