O4-review/random-number-generator.md

+# Random number generator fix (https://git.ligo.org/lscsoft/bilby/-/merge_requests/1273)
+
+For a detailed discussion see the linked merge request. To summarize, using the global `numpy` RNG with multiprocessing means that each thread uses the same random sequence. The only place in `Bilby` analyses of real data that this is relevant is in the reconstruction of the marginalized parameters in post-processing and leads to non-independent samples for any marginalized parameters.
+
+The most obvious display of this is in the network optimal SNR where we see clustering of the values in trace plots, e.g.,
+
+![image.png](uploads/c777ed14cedb13d58111dc68afe68fb6/image.png)
+
+after implementing this fix the same analysis gives the following trace
+
+![image.png](uploads/dc1f51d52d30b266bfaa0cf2599ea696/image.png)
+
+The number of points is slightly different because a different random downsampling from nested samples to posterior samples was used.
+
+This will require an update to `bilby_pipe` after the release of `Bilby` is made to make sure the random seed is set properly.
\ No newline at end of file