O4-review/relative-binning.md

+## Likelihood differences
+
+Compute likelihood difference for
+
+- 64s NSBH pp-test
+- Good BNS analysis
+- Bad BNS analysis
+
+## [Unit testing](https://git.ligo.org/lscsoft/bilby/-/blob/master/test/gw/likelihood/relative_binning_test.py)
+
+As part of the `Bilby` CI unit testing, we verify that the binned likelihood agrees with the regular likelihood the reference point for a range of cases.
+We also verify that the likelihood is close to the regular model for 100 points drawn from a prior distribution.
+The final test is the optimization to find the reference parameters gives a good likelihood match after the optimization.
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