Compound models and Pearson residuals for single-cell RNA-seq data without UMIs

Recent work employed Pearson residuals from Poisson or negative binomial models to normalize UMI data. To extend this approach to non-UMI data, we model the additional amplification step with a compound distribution: we assume that sequenced RNA molecules follow a negative binomial distribution, and are then replicated following an amplification distribution. We show how this model leads to compound Pearson residuals, which yield meaningful gene selection and embeddings of Smart-seq2 datasets. Further, we suggest that amplification distributions across several sequencing protocols can be described by a broken power law. The resulting compound model captures previously unexplained overdispersion and zero-inflation patterns in non-UMI data.