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-based scRNA-seq data. To extend this approach to non-UMI data, we model the amplification step with a compound distribution: we assume that captured RNA molecules follow a negative binomial distribution and are replicated following an amplification distribution. This model leads to compound Pearson residuals, yielding meaningful gene selection and embeddings of Smart-seq2 datasets. Furthermore, we show 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.