Hi,

I am trying to understand and compare the DESeq2 model and the BNB-R (https://github.com/siamakz/BNBR) model. The corresponding references are:

• DESeq2: Love, M. I., Huber, W., & Anders, S. (2014). Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biology, 15(12), 550. https://doi.org/10.1186/s13059-014-0550-8
• BNB-R: Dadaneh, S. Z., Zhou, M., & Qian, X. (2018). Bayesian negative binomial regression for differential expression with confounding factors. Bioinformatics, 34(19), 3349–3356. https://doi.org/10.1093/bioinformatics/bty330

My understanding of the BNB-R model is that it regards the sample-specific size factor r_j of the negative binomial distribution as a parameter that has to be estimated through Bayesian inference (i.e. sampling from its posterior). In DESeq2, there is a pre-estimated sample-specific size factor s_j included in the mean, but there is also the dispersion parameter alpha_i. Therefore, am I right that DESeq2 imposes additional overdispersion (having the pre-estimated size factors s_j as well as alpha_i)?

I don't follow what you mean by additional overdispersion. The library size factor is fixed across genes but unknown. We estimate it, and then treat it as fixed. I do think that it's a good idea to build in more conservative behavior by acknowledging that the size factor is not known. When I give talks about effect sizes, I mention that one way to do this post-hoc is to use a lfcThreshold, which avoids reporting genes which have effect sizes close to 0. If we estimate the size factors wrong, the genes with effect size close to 0 will be the first to be wrong, while the ones farthest from 0 are the safest.