The reason for the power of N might have to do with extreme value statistics. Tomorrow I'll take s detailed look. Sent from my iPhone On Sep 8, 2013, at 18:33, Keitaro Yamashita wrote:

Dear all,

Thank you for your replies. I have already had a look at Read (1999) paper, but I could not find direct explanation of this implementation (or what the message in the code explains).

Thanks to an advice of my friend, I understand that what the code does is something like likelihood-ratio test. The reason why taking square root is because cumulative distribution function of chi-square distribution with freedom of one is erf(sqrt(x/2)). However, I still do not understand the reason why it is raised to the power of N (**N). I would be grateful if you explained the reason.

Best regards, Keitaro

2013/9/6 Peter Zwart :

...

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 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 _______________________________________________ cctbxbb mailing list [email protected] http://phenix-online.org/mailman/listinfo/cctbxbb

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