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. 2021 Oct 20;12:6106. doi: 10.1038/s41467-021-26328-2

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a A bar chart of average log-likelihood of the three types of distribution fitted to PBMC single-cell RNA-seq data. The genes were split by DEGs (red; n = 1723) and non-DEGs (blue; n = 1496). b Comparison of the distance of the estimated mode to the true mode (y-axis) per distribution type (x-axis). The standard boxplot notation was used (lower/upper hinges— first/third quartiles; whiskers extend from the hinges to the largest/lowest values no further than 1.5 * inter-quartile ranges). c Pairwise comparison of per-gene log-likelihood of log-normal distribution (y-axis) and that of normal (x-axis; top) and negative binomial distribution (x-axis; bottom). The genes were split into non-DEGs (left) and DEGs (right). d Density plots for raw-counts (red) and optimized log-normal (green), normal (blue), and negative binomial distribution (purple) for four example genes (gene name at the top) with low maximum log-likelihood for normal distribution. e, f Maximum log-likelihood values (e) and root mean squared error (root MSE: f) of each gene for log-normal (y-axis) and negative binomial (x-axis) convolutions of T = 8 cell types, applied to TCGA-MESO (left) and TCGA-SARC (right) data.