Issues-with-covaraince-matrix.md

@@ -65,8 +65,7 @@ A similar plot for the GW190412 event (top 5 [PE samples](https://git.ligo.org/p
 | 31.1000 | 10.2668 | 0.0572   |  0.6907 |  -48630.0520   | 6.7  |
 | 33.7223 | 9.7035  | 0.3080   | -0.0899 |  -48630.0727   | 7.0  |
 
-<img src="uploads/c7df73e51383e0485310fe22cd0f536c/beta_lambda_all_3_.png"  width="440" > 
-
+<img src="uploads/b70121bb673f3f1ba9966c123f598f90/beta_lambda_all.png"  width="440" > 
 
 The effective-rank of the covariance matrix needs to be tuned for each event using a diagnostic plot such as those shown above. 
 
@@ -75,5 +74,12 @@ The effective-rank of the covariance matrix needs to be tuned for each event usi
 <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 which are reported in the above tables. 
+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). 
+
+## Rank versus $`gamma`$ 
+
+<img src="uploads/2cf16becd150e692ebd02d0453db7b81/rank_gamma_gw190412.png"  width="440" >
+<img src="uploads/721d9d4434d730738e225e5bbf793056/rank_gamma_gw190814.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.