Issues-with-covaraince-matrix.md

@@ -69,17 +69,22 @@ A similar plot for the GW190412 event (top 5 [PE samples](https://git.ligo.org/p
 
 The effective-rank of the covariance matrix needs to be tuned for each event using a diagnostic plot such as those shown above. 
 
-## Rank versus $`\beta`$ for off-source samples
+## $`\beta`$ for off-source samples versus rank
 
 <img src="uploads/c3f7f42f77a670ae2bc6f9908e7765f9/beta_lambda_nalpha.png"  width="440" >
 <img src="uploads/cdfd3a190ebfed40bdfc51d574b38a88/beta_lambda_nalpha.png"  width="440" >
 
-The above figures show the variation in $`\beta`$ with respect to the rank of the covariance matrix for off-source samples. The plots are produced using the off-source samples obtained for maximum likelihood samples ( reported in the above tables). 
+The above figures show the variation in $`\beta`$ for off-source samples with respect to the rank of the covariance matrix. The plots are produced using the off-source samples obtained for maximum likelihood samples ( reported in the above tables). 
 
-## Rank versus $`\gamma`$ 
+## $`\gamma`$ versus rank 
 
 <img src="uploads/b79e18a4ee6bd247d58d3aab806b8178/rank_gamma_gw190412_2_.png"  width="440" >
 <img src="uploads/7d12acced7e7ff9ab2b947bad9bfca07/rank_gamma_gw190814_1_.png"  width="440" >
 
 The above figures show the variation in $`\gamma`$ with respect to the rank of the covariance matrix for off-source samples.  The intrinsic parameter of maximum likelihood samples (reported in the above tables) are used to produce the plots. 
 
+## LLR22 versus rank
+
+<img src="uploads/a2d44c117101b73d3feb36e291514f3e/LLR22_lambda_onsource_gw190412.png"  width="440" >
+
+The figure show the variation of LLR22 versus the rank of the covariance matrix. These results produced using the 5 largest likelihood samples.  
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