Calculation of estimated biological variation
Genes that have been normalized by Normalize Single Cell Data have an expected variance of![$ \sim1$](img40.gif)
We define the `estimated biological variation'
in a normalized sample to be the fraction of the total variance that is above the expected variance due to random noise for each gene
![$\displaystyle v_{\mathrm{bio}} = \frac{\sum_g \max(\mathrm{Var}(z_g) - 1,0)}{\sum_g (\mathrm{Var}(z_g))}.$](img42.gif)
Here, are the normalized expressions of gene
. Note that this estimate assumes that all variation remaining after normalization is of `biological' origin. This is unlikely in practice, and the estimate will often be too high.