deletions | additions       diff --git a/The combined likelihood test.tex b/The combined likelihood test.tex  index c85a3fb..ed0b904 100644  --- a/The combined likelihood test.tex  +++ b/The combined likelihood test.tex 
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TODO: write about likelihood ratio test, asymtotically distributed as |Chi^2_1|.   \[  \textrm{L}\left( D_{h} \left| \alpha_h, \beta_h, \Phi_i, \eta_j,  \Upsilon_\bullet \right. \right) = \prod_i \left[ \Pr_{\mathrm{BNB}} \left( X = x_{ij} \left| \lambda_{hi}, \Phi_i, \eta_j \right. \right) \prod_k \Pr_{\mathrm{BB-mix}}\left(Y_{ik} = y_{ik} \left| p_{h}, n_{ik}, \Upsilon_i \right. \right) \right] \]