Inference after latent variable estimation for single-cell RNA sequencing data

In the analysis of single-cell RNA sequencing data, researchers often characterize the variation between cells by estimating a latent variable, such as cell type or pseudotime, representing some aspect of the cell's state. They then test each gene for association with the estimated latent variable. If the same data are used for both of these steps, then standard methods for computing p-values in the second step will fail to achieve statistical guarantees such as Type 1 error control. Furthermore, approaches such as sample splitting that can be applied to solve similar problems in other settings are not applicable in this context. In this article, we introduce count splitting, a flexible framework that allows us to carry out valid inference in this setting, for virtually any latent variable estimation technique and inference approach, under a Poisson assumption. We demonstrate the Type 1 error control and power of count splitting in a simulation study and apply count splitting to a data set of pluripotent stem cells differentiating to cardiomyocytes.

A joint characterization of the multinomial distribution and the Poisson process

It has been recently proved that if N, X 1, X 2, … are non-constant mutually independent random variables with X 1,X 2, … identically distributed and N non-negative and integer-valued, then the independence of and implies that X 1 is Bernoulli and N is Poisson. A well-known theorem in point process theory due to Fichtner characterizes a Poisson process in terms of a sum of independent thinnings. In the present article, simultaneous generalizations of both of these results are provided, including a joint characterization of the multinomial distribution and the Poisson process.