deletions | additions       diff --git a/Correcting read depth and GC.tex b/Correcting read depth and GC.tex  index c82ac23..e5f855d 100644  --- a/Correcting read depth and GC.tex  +++ b/Correcting read depth and GC.tex 
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\subsubsection{Fitting adjustment coefficients}  For each target region $j$, we count the total number of reads $v_j$ and calculate the GC content $w_j$. Then, for each individual $i$, we fit find maximum likelihood estimates of the  coefficients $a_{0i}, a_{1i}, \ldots, b_{4i} $ that maximize which define  the likelihood of adjusted total read depth $T^{*}_{i,j}$, given  the observed read  counts given the adjusted expected counts, $T^{*}_{ij}$: and GC content:  \[  \textrm{L}\left( D_i \left| a_{0i}, \textrm{L}\left(a_{0i},  a_{1i}, \ldots, b_{4i} \left| D_i  \right. \right) \right )  = \prod_j \Pr_{\mathrm{Pois}} \left(X_{ij} = x_{ij} \left| T^{*}_{ij} \right. \right)\\ \]  \[  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)