Entering edit mode
Hi,
I am sorry that I was not able to find the correct way to type in the math formula directly. Thus, I typed the question in Latex/Overleaf and added it as an image below. Thanks a lot for the help!
Best regards,
Xinwei
Thanks, Gordon! Doesn't the formula in edgeR user guide have u intead of E(u) on the right side? Or do I misunderstand the notation?
\mu_{gi} is a constant, not a random variable. See the Methods and Materials section of
McCarthy, DJ, Chen, Y, Smyth, GK (2012). Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation. Nucleic Acids Research 40, 4288-4297. https://doi.org/10.1093/nar/gks042
Thanks for the paper! I still do not understand why \mu_{gi} is a constant. As each biological replicate i has a different \mu_{gi}, \mu_{gi} seems to be a random variable. The Methods and Materials section of paper also mentions "treating the \pi_{gi} as gamma distributed". Since \mu_{gi} = N_{i} * \pi_{gi}, if \pi_{gi} is gamma-distributed random variable, why is \mu_{gi} a constant?
The first display equation in the Materials and Methods section is slightly misleading. It should read
E(y_{gi}) = \mu_{gi} = N_i E(\pi_{gi})
We should perhaps have introduced a new symbol for E(\pi_{gi}), but the paper already has a lot of mathematics for an article in the NAR journal.
The \mu_{gi} only differ between replicates if N_i varies.
Thanks a lot, Gordon! I think I understand it now. In this definition, \mu_{gi} is indeed a constant w.r.t. \pi_{gi}.
In addition to the paper you mentioned above and other papers cited in edgeR user guide, are there any other sources (e.g. a book chapter or a video lecture) showing the step-by-step breakdown of the math behind edgeR?
Thanks again!