update the RB fitting method to compensate for the standard deviation induced from the random number generator

[NoureldinYosri]

changing the RB fitting method to 1) scale the estimated error to remove the effect of the std of the random number generator 2) take into account the standard deviation of the error. this means that instead of fitting a curve to $(x_i, y_i)$ it will fit a curve that passes through $(x_i, \hat{y_i})$ where $\hat{y_i} \in [y_i - \sigma_i, y_i + \sigma_i]$

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.50%. Comparing base (dc69fa1) to head (12ea768).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #7562   +/-   ##
=======================================
  Coverage   97.50%   97.50%           
=======================================
  Files        1103     1103           
  Lines       99695    99716   +21     
=======================================
+ Hits        97209    97230   +21     
  Misses       2486     2486           

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[mhucka]

@NoureldinYosri Could you please add a description to this PR? As a matter of best practices, we shouldn't leave PR descriptions empty.

[mhucka]

LGTM pending the addition of a description to this PR and double-checking whether the test function name was really intended to be as it is written.

[eliottrosenberg]

Thanks, @NoureldinYosri! But I don't think this fixed the variance problem. I tested it in this colab.

[NoureldinYosri]

@eliottrosenberg the results from running the internal RB are not independent, they are correlated. if you rerun the notebook but turnoff parameter updates you will get similar std https://colab.research.google.com/drive/1U6yDZBNDU4wSqjxVukHCz1mbwvyj7PQO#scrollTo=Fwi7fjYUBpr5

[eliottrosenberg]

Approving so that we can merge this, but I don't think the investigation is done.