Problem understanding formulas in the paper

[AbelSILLY]

Hello,

I'm thinking about using your software but I would like first to understand fully what's behind. So my question is more about the maths behind the software than with the software itself (sorry if this is the wrong place for such a question).
When reading the article I'm not sure to understand how the $\hat{\delta}_{WLS}$ is calculated.

The formula gives

$\frac{\sum_{i\in C_0}\frac{\Delta_i}{\hat{\nu}{i0}^2} + \sum{i\in C_1}\frac{\Delta_i - \hat{l}1}{\hat{\nu}{i1}^2} + \sum_{i\in C_2}\frac{\Delta_i - \hat{l}2}{\hat{\nu}{i2}^2}}{\sum_{i\in C_0}\frac{1}{\hat{\nu}{i0}^2} + \sum{i\in C_1}\frac{1}{\hat{\nu}{i1}^2} + \sum{i\in C_2}\frac{1}{\hat{\nu}_{i2}^2}}$

But I don't understand how one can compute this formula from the data. Maybe I missunderstood but I thought that the $C_r,r=1,2,3$ were not "accessible" sets in the sense that we don't know a priori if a taxon is differentially abundant or no (it's the point of the analysis) and hence I don't understand how we can sum on those sets.

Did I missunderstood something or could you explain it to me ?

Thanks for your time.

Best regards,

Abel

PS: sorry if the formula is not well written there seems to be a problem in the preview