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Generalize Bayesian DA to N-dimensions #352

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Gabriel-p opened this issue Sep 20, 2017 · 0 comments
Closed

Generalize Bayesian DA to N-dimensions #352

Gabriel-p opened this issue Sep 20, 2017 · 0 comments

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@Gabriel-p
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Gabriel-p commented Sep 20, 2017

Left over from #24. Things I changed:

  1. likelihood() core (obviously)
  2. added reg_data() function to store data in the proper format to pass to likelihood()
  3. If a field region has more stars than the cluster region, previously the algorithm passed the entire cluster region with no random removal of field stars (to obtain the likelihood of being a cluster member). This resulted in large likelihoods for all stars of being a cluster member, which does not seem right. Now I simply assign zero likelihoods to all stars within the cluster region. This is both faster and statistically correct.
  4. The likelihood used for each star within the cluster region is
    captura realizada el 2017-09-21 14 28 55
    and the full Bayesian probability is (A and B are incorrectly swapped in Perren et al. (2015)):
    codecogseqn
    Both L_X and MP_j have terms N_X in them and they cancel out, so the final MP_j equation can be written as:
    codecogseqn 1
    This means no n_cl term needs to be defined, which (combined with the change mentioned above) greatly improves the results for clusters where the cluster region contains fewer star than the field regions. See for example B48 (left: old DA, right: new one)
    captura realizada el 2017-09-21 14 38 26
  5. Previously the same likelihood between a field region and the full cluster region was calculated bayesda_runs, which made no sense since it is the exact same operation performed over and over again. Now this operation is performed only once per field region, before both for blocks.
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