deletions | additions       diff --git a/Estimating overdispersion parameters.tex b/Estimating overdispersion parameters.tex  index 2660697..33baf66 100644  --- a/Estimating overdispersion parameters.tex  +++ b/Estimating overdispersion parameters.tex 
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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 $\eta_j$ using the equation  %\[  %\textrm{L}\left(\eta_j \[  \textrm{L}\left(\eta_j  \left| D \right. \right) = \prod_i \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} %\left| \left|  \lambda = T^*_{ij}, \Phi_i, \eta_j \right. \right) \right] %\] \]  and then $\Phi_i $\Phi_i$  using the equation %\[  %\textrm{L}\left(\Phi_i \[  \textrm{L}\left(\Phi_i  \left| D \right. \right) = \prod_j \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} %\left| \left|  \lambda = T^*_{ij}, \Phi_i, \eta_j \right. \right) \right] %\] \]  \subsubsection{Beta-Binomial}