In the paper of Love (2014) it says about the initial GLM:

To get a gene-wise dis- persion estimate for a gene i, we start by fitting a negative binomial GLM without an LFC prior for the design matrix X to the gene’s count data. This GLM uses a rough method-of-moments estimate of dispersion, based on the within-group variances and means.

What does it mean to fit a negative binomial GLM 'WITHOUT AN LFC PRIOR FOR THE DESIGN MATRIX X'? If we are fitting a negative binomial GLM then we would have to estimate the mean and the dispersion parameters. So where are the LFC priors taking place and what are they? And how do we get the initial fitted values \hat{\mu}_ij^0?

I would be very glad to get an explanation for this or a paper/book to read this in.

Just think, standard GLM as you would get with glm.nb.

We ended up breaking out the prior on coefficients into a separate function, so you can totally ignore the LFC prior part of the 2014 DESeq2 paper.