deletions | additions       diff --git a/Estimating overdispersion parameters.tex b/Estimating overdispersion parameters.tex  index 650ed7e..20c5888 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 $\Phi_i$ $\Omega_i$  we need to sum the log likelihood across all regions. This presents a problem, as $\eta_j$ $\phi_j$  must also be estimated for each region. We therefore interatively estimate $\eta_j$ $\phi_j$  by first finding a maximum likelihood estimate for $\eta_j$ $\phi_j$  for each region using the equation: \[  \textrm{L}\left(\eta_j \textrm{L}\left(\phi_j  \left| D \right. \right) = \prod_i \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} \left| \lambda = T^*_{ij}, \Phi_i, \eta_j \Omega_i, \phi_j  \right. \right) \right] \]  and then finding a maximum likelihood estimate for $\Phi_i$ $\Omega_i$  for each individual using the 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]