deletions | additions       diff --git a/Estimating overdispersion parameters.tex b/Estimating overdispersion parameters.tex  index 37bd808..1e3669f 100644  --- a/Estimating overdispersion parameters.tex  +++ b/Estimating overdispersion parameters.tex 
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\subsubsection{Beta-Negative-Binomial}  To find the maximum likelihood estimate of $\Phi_i$ we need to sum the likelihood across all regions. This presents a problem, as $\eta_j$ must also be estimated for each region. We therefore interatively estimate $\eta_j$ by first finding a maximum likelihood estimate for $\eta_j$ for each region  using the equation equation:  \[  \textrm{L}\left(\eta_j \left| D \right. \right) = \prod_i \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} \left| \lambda = T^*_{ij}, \Phi_i, \eta_j \right. \right) \right]   \]  and then finding a maximum likelihood estimate for  $\Phi_i$ for each individual  using the equation equation:  \[  \textrm{L}\left(\Phi_i \left| D \right. \right) = \prod_j \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} \left| \lambda = T^*_{ij}, \Phi_i, \eta_j \right. \right) \right]   \]  We repeat this iterative procedure until the improvement in likelihood becomes negligable.  \subsubsection{Beta-Binomial}  To find the maximum likelihood estimate of $\Upsilon_i$ we sum the allele specific likelihood across all regions. We again assume there is no genetic effect, so $p$ = 0.5.