# [cctbxbb] Model based outlier calculation in mmtbx.scaling.outlier_rejection

Peter Zwart PHZwart at lbl.gov
Thu Sep 5 09:26:37 PDT 2013

```Hi,

It has been a while since I wrote this and you could potentially be right
that I forget to devide by the second derivative, I'll have a look.

P

On 5 September 2013 02:31, Keitaro Yamashita <k.yamashita at spring8.or.jp>wrote:

> 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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>

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P.H. Zwart
Research Scientist
Berkeley Center for Structural Biology
Lawrence Berkeley National Laboratories
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