deletions | additions       diff --git a/Estimating overdispersion parameters.tex b/Estimating overdispersion parameters.tex  index 786563b..9912b77 100644  --- a/Estimating overdispersion parameters.tex  +++ b/Estimating overdispersion parameters.tex 
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\subsubsection{Beta-Binomial}  We calculate the genome-wide likelihood of $\Upsilon_i$ by taking the product of likelihoods from all target region SNPs that are heterozygous in individual $i$. We again assume there is no genetic effect, so $p$ = 0.5, and we find the maximum likelihood estimate of $\Upsilon_i$ numerically. numerically:  \[  \textrm{L}\left(\Upsilon_i \left| D \right. \right) = \prod_k \Pr_{\mathrm{BB-mix}} \left( Y = y_{ik} \left| n_{ik}, p = 0.5, \Upsilon_i \right. \right) \\