[cctbxbb] Question about sigma(I) calculation in merge_equivalents

[Keitaro Yamashita]

Dear CCTBX developers,

I have a question about the method in CCTBX to calculate
sigma(averaged I) when merging.

In cctbx/miller/merge_equivalents.h (line 594 in phenix-dev-1148),
sigma(averaged I)^2 will be calculated by
max(mv.gsl_stats_wvariance()/values.size(), 1/mv.sum_weights()).
It takes maximum value of the two options.

I know the latter equation - this is just sigma(averaged I)^2 =
1/sum(w), where w = 1/sigma(I)^2.
And I believe this equation is widely used in other crystallographic
programs e.g. XDS.

The former is, according to the comment in the code, the emulation of
gsl_stats_wvariance, and we can find the information from gsl website:
http://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html

I don't know how this "wvariance" is derived.
Is it a better estimate of sigma(averaged I)?
Why does it take the maximum from the two options?

I would like to know the theory of this sigma calculation in CCTBX.


Best regards,
Keitaro