Issues-with-covaraince-matrix.md

@@ -67,6 +67,17 @@ A similar plot for the GW190412 event (top 5 [PE samples](https://git.ligo.org/p
 
 <img src="uploads/c7df73e51383e0485310fe22cd0f536c/beta_lambda_all_3_.png"  width="440" > 
 
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 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
+<img src="uploads/fe96e535c7f921b3b65f8ba209c47d68/beta_lambda_nalpha_2_.png"  width="440" >
+<img src="uploads/27ac1831fe2b94185cc51bcdba11d53c/beta_lambda_nalpha_3_.png"  width="440" >
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+The right plot shows ra