I am learning how limma package works and diving into the world of bayesian statistics and linear algebra. Feeling frustrated because, I cannot fully explain what the these formula below mean. I am wondering whether my understanding of the name of variable is correct.

𝛽 ̂_𝑗𝑘=𝜎_𝑗^2 𝐶^𝑇 (𝑋^𝑇 𝑉_𝑗 𝑋)^(−1) 𝐶 : linear model

(𝑠_𝑗 ) ̃^2=(𝑑_0 𝑠_0^2+𝑑_𝑗 𝑠_𝑗^2) / (𝑑_0+𝑑_𝑗 ) : empirical bayes

𝑡 ̃_𝑗𝑘=𝛽 ̂_𝑗𝑘/(𝑢_𝑗𝑘 𝑠 ̃_𝑗 ) : moderated-t

[ 𝛽 ̂_𝑗𝑘 --> maximum likelihood estimator ] [ 𝜎_𝑗^2 --> variance ] [ X --> design matrix ] [ C --> contrast matrix ] [ V --> weight matrix ]

[ (𝑠_𝑗 ) ̃^2 --> residual variance ] [ 𝑑_0, 𝑑_𝑗 --> degrees of freedom ] [ 𝑠_0, 𝑠_𝑗 --> variance ]

[ 𝑡 ̃_𝑗𝑘 --> t value ] [ 𝑢_𝑗𝑘 --> standard deviation ]

Are my understanding true ?

I would appreciate it if someone could answer. And very sorry for hard to see the formula.... Please see accurate formula in "http://www.uvm.edu/~rsingle/JournalClub/papers/Smyth-SAGMB-2004_eBayes+microarray.pdf"