corrected missing sigma factor in posterior sampler

1. Rapidpe samples are generated with Gaussians of standard deviation=grid_size and amplitude=Marginlaized_Likelihood. During the implementation, we call numpy.random.normal function which has an amplitude
   $1/\sqrt{2\pi\sigma}$
   due to normalization. So, wherever we modify the script to have the amplitude=Marginlaized_Likelihood, need a correction factor of
   $\sqrt{2\pi\sigma}$
   .

• corrected missing
  $\sqrt{2\pi\sigma}$
  factor in posterior sampling and evidence calculation. Here is a simplified demonstration of this correction https://git.ligo.org/rapidpe-rift/rapidpe_rift_review_o4/-/blob/main/rapidpe_amr_review/Notebooks/NormalizationCorrection.ipynb

2. Rapidpe posterior samples are generated in mchirp-q (or mchirp-mtotal) with a prior uniform in mass1-mass2 as a function of mchirp-q(or mchirp-mtotal). To get the mass1, and mass2 samples we need to convert the mchirp-q (or mchirp-mtotal) sample to mass1-mass2 and assign the prior of the corresponding mchirp-q(or mchirp-mtotal) as a weight for each samples.

• corrected the weight of m1-m2 samples in the posterior plot

3. We usually save weighted samples. Additionally save posterior samples after resampling from weighted samples.

• save posterior samples in addition to weighted posterior samples

Review wiki with these corrections applied: https://git.ligo.org/rapidpe-rift/rapidpe_rift_review_o4/-/wikis/AMR-Review/Review-Version-2

Review wiki before these corrections: https://git.ligo.org/rapidpe-rift/rapidpe_rift_review_o4/-/wikis/AMR-Review

• Comparison run between this version and the previous version:

  • new version: https://ldas-jobs.ligo.caltech.edu/~vinaya.valsan/RapidPE/posterior_correction/S231213ap_new/summarypage.html

  • current online version: https://ldas-jobs.ligo.caltech.edu/~emfollow/online_pe/S231213ap/rapidpe/summarypage.html

  • new version: https://ldas-jobs.ligo.caltech.edu/~vinaya.valsan/RapidPE/posterior_correction/S231231ag_new_spin2/summarypage.html

  • current online version: https://ldas-jobs.ligo.caltech.edu/~emfollow/online_pe/S231231ag/rapidpe/summarypage.html

requested review from @caitlin.rose

assigned to @vinaya.valsan

marked the checklist item corrected missing \sqrt{2\pi\sigma} factor in posterior sampling and evidence calculation as completed

marked the checklist item corrected the weight of m1-m2 samples in the posterior plot as completed

changed title from corrected missing sigma factor in posterior sampler to corrected missing sigma factor in posterior sampler(3)

mentioned in issue #123 (closed)

marked this merge request as draft

added 18 commits

• aa186616...98c25b57 - 17 commits from branch rapidpe-rift:main
• e4dc9b65 - corrected missing sigma factor in posterior sampler

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added 180 commits

• e4dc9b65...970faf98 - 170 earlier commits
• 06675a93 - bug fix in search_bias json
• 74b2126a - remove inf and nan from margll
• 0db5b87d - Incrementing version to 0.6.2
• 729da44f - updated fmin_template for pycbc
• bf1cd588 - incrementing version to 0.6.3
• 8348fb8e - updated initial region bounds for bbh
• 7ee2c128 - updated logic for mapping to injection for MDC
• ebf25388 - incrementing version to 0.6.4
• a28be9ad - saving grid_info_dict in a h5 file
• 0e3bb1aa - corrected missing sigma factor in posterior sampler

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added 263 commits

• 0e3bb1aa...80576fad - 260 commits from branch rapidpe-rift:main
• 07754cc3 - incrementing to 0.3.1
• e8020d5c - saving grid_info_dict in a h5 file
• 5eb899fa - corrected missing sigma factor in posterior sampler

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added 1 commit

• 62fd661a - fixed p_per_grid

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added 1 commit

• 3202fe23 - updated

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marked the checklist item save posterior samples instead of weighted samples #124 as completed

removed review request for @caitlin.rose

changed the description

changed the description

requested review from @daniel.wysocki

changed title from Draft: corrected missing sigma factor in posterior sampler(3) to Draft: corrected missing sigma factor in posterior sampler