Dear cctbx developers,

I am interested in the implementation of model-based reflection
outlier rejection. As I read the code
mmtbx/scaling/outlier_rejection.py (lines 244-351), I noticed that
maybe there was a discrepancy between what log_message explained and
the actual code. The log_message in the code says:

> Outliers are rejected on the basis of the assumption that a scaled
> log likelihood differnce 2(log[P(Fobs)]-log[P(Fmode)])/Q\" is distributed
> according to a Chi-square distribution (Q\" is equal to the second
> derivative of the log likelihood function of the mode of the
> distribution).
> The outlier threshold of the p-value relates to the p-value of the
> extreme value distribution of the chi-square distribution.

while actual p_value is calculated for each hkl as
p_value = 1 - erf(sqrt(LLG))**N,
where
LLG = log p(F=Fbar | Fmodel) - log p(F=Fobs | Fmodel),
and N is the number of reflections. Here, Fbar is F which
gives the maximum value of p(F | Fmodel). At least, Q (the second
derivative of p(F=Fbar | Fmodel)) is not used in the actual
calculation.

Could someone please explain the meaning of the actual calculation?
Why taking square-root and raising erf() result to the power of N?

Thank you very much,
Keitaro
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