On the problem of scoring genes for evidence of changes in the distribution of single-cell expression, we introduce an empirical Bayesian mixture approach and evaluate its operating characteristics in a range of numerical experiments. The proposed approach leverages cell-subtype structure revealed in cluster analysis in order to boost gene-level information on expression changes. Cell clustering informs gene-level analysis through a specially-constructed prior distribution over pairs of multinomial probability vectors; this prior meshes with available model-based tools that score patterns of differential expression over multiple subtypes. We derive an explicit formula for the posterior probability that a gene has the same distribution in two cellular conditions, allowing for a gene-specific mixture over subtypes in each condition. Advantage is gained by the compositional structure of the model not only in which a host of gene-specific mixture components are allowed but also in which the mixing proportions are constrained at the whole cell level. This structure leads to a novel form of information sharing through which the cell-clustering results support gene-level scoring of differential distribution. The result, according to our numerical experiments, is improved sensitivity compared to several standard approaches for detecting distributional expression changes.
Keywords: Local false discovery rate; clustering; double Dirichlet mixture; empirical Bayes; mixture model.