Parallel-Bilby-Phase-Marginalisation-Review.md

 # Phase Marginalisation with Parallel Bilby
 
+
+## PP-test results
+|  | *Phase Margin = ON* | *Phase Margin = OFF* | 
+| ------ | ------ |  ------ |
+| PP-test | ![pp_test_phase_marginalisation_on](uploads/fdc426f0efa813babc9598dab8cdc09b/pp_test_phase_marginalisation_on.png) | ![pp_test_phase_marginalisation_off](uploads/3fe842bbdbbba663e6cf82f569f8c01a/pp_test_phase_marginalisation_off.png) |
+| Meta | ![phase_marginalisation_on_meta](uploads/3476450a96b1924f155139e89cbcd888/phase_marginalisation_on_meta.png) | ![phase_marginalisation_off_meta](uploads/330cdb3c4d57f0a5f2bca270404ac580/phase_marginalisation_off_meta.png) |
+These demonstrate that parallel bilby is unbaised when analysing with/without phase marginalisation. 
+
 ## PP-test setup
 
 * Smapled a set of 100 injection parameters from the bilby `4s` prior. 
@@ -22,19 +30,14 @@ nodes=1
 n-tasks-per-node=16
 ```
 
-## PP-test results
-|  | *Phase Margin = ON* | *Phase Margin = OFF* | 
-| ------ | ------ |  ------ |
-| PP-test | ![pp_test_phase_marginalisation_on](uploads/fdc426f0efa813babc9598dab8cdc09b/pp_test_phase_marginalisation_on.png) | ![pp_test_phase_marginalisation_off](uploads/3fe842bbdbbba663e6cf82f569f8c01a/pp_test_phase_marginalisation_off.png) |
-| Meta | ![phase_marginalisation_on_meta](uploads/3476450a96b1924f155139e89cbcd888/phase_marginalisation_on_meta.png) | ![phase_marginalisation_off_meta](uploads/330cdb3c4d57f0a5f2bca270404ac580/phase_marginalisation_off_meta.png) |
 
 ## Histogramming the Evidence Residuals
 Below is a histogram of the evidence residuals (logZ_on - logZ_off) from the above runs. 
 ![Evidence Residual](uploads/fd9915b107dc3da5178824e681d2ea0f/test.png)
-This demonstrates that the LogZ are relatively the same, with a slight difference, most likely due to sampling. 
+This demonstrates that the LogZ are relatively the same, with a slight difference, most likely due to sampling. Note that the sigma of the Gaussian fit is close to the typical evidence uncertainty reported by dynesty
 
 ## Example Corner
-The following corner plot is from an injection with SNRs of {H1: 12.89, L1: 10.48}. Note that althought the posteriors look a bit messy, this has been made with one run, rather than combining the results from multiple runs.
+The following corner plot is from an injection with SNRs of {H1: 12.89, L1: 10.48}. Note that although the posteriors look a bit messy, this has been made with one run, rather than combining the results from multiple runs.
 ![injection_70_corner](uploads/6f302dc258e8f06670b0a3e07a9906b7/injection_70_corner.png)