deletions | additions       diff --git a/Correcting read depth and GC.tex b/Correcting read depth and GC.tex  index 46bbc2a..daa57b8 100644  --- a/Correcting read depth and GC.tex  +++ b/Correcting read depth and GC.tex 
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For each target region, $j$, we count the total number of reads across individuals, $v_j = \sum_i x_{ij}$, and calculate the GC content, $w_j$. Then, for each individual $i$, we find maximum likelihood estimates of the coefficients $a_{0i}, a_{1i}, \ldots, b_{4i}$ that define the adjusted total read depth $T^{*}_{i,j}$, given the observed read counts and GC content:  \[  \textrm{L}\left(a_{0i}, a_{1i}, \ldots, b_{4i} \left| D_i \right. \right ) = \prod_j \Pr_{\mathrm{Pois}} \left(X_{ij} \left(X  = x_{ij} \left| T^{*}_{ij} \right. \right)\\ \]  \[  T^{*}_{ij} = \exp\left(a_{0i} + a_{1i} w_j + a_{2i} w_j^2 + a_{3i} w_j^3 + a_{4i} w_j^4 \right) \left(b_{1i} v_j + b_{2i} v_j^2 + b_{3i} v_j^3 + b_{4i} v_j^4 \right)