Update 08.27.2018 -- Run 9 pp: bin-by-bin test

In a recent internal meeting it was suggested that since the corrections in the unfolding process were so small, it might be prudent to switch to a bin-by-bin correction since the process is far more transparent than unfolding.  Below I compare unfolded and backfolded distributions to Pythia8 and data respectively for 3 different correction schemes: Bayesian unfolding, SVD unfolding, and bin-by-bin corrections.

Note that the unfolded gamma-rich distributions have been corrected for the gamma-rich purity.  It would seem that all 3 correction schemes produce similar (if not consistent to nearly identical) results.  However, the bin-by-bin scheme assumes that bin migration is negligible; I'm concerned that we might not be able to assume that considering the jet energy resolution (see links below), especially at large pTjet...

https://drupal.star.bnl.gov/STAR/blog/dmawxc/update-08072018-run-9-embedding-jet-energy-resolution-r-02-03-04-and-05
https://drupal.star.bnl.gov/STAR/blog/dmawxc/update-08132018-run-9-embedding-updated-jet-matching-efficiency-and-jet-energy-resolutio

The individual plots that went into the above ones have been attached, and so have the corresponding ROOT files.

Update [08.28.2018]:
to get a more quantitative idea of the size of the corrections for each method, see this post:

https://drupal.star.bnl.gov/STAR/blog/dmawxc/update-08282018-run-9-pp-raw-vs-corrected-data-bin-bin-test