The rotation merge fitted var = a*s2 + b^2*<I>^2 from three separate medians (s2, I2, dev2) per
bin of I2. A median of dev2 over observations whose variances differ is not 0.455 times their mean
variance, so the ratio of medians read a too low and b too high: on the scaled fulls of 28 sets
(in-house, open and private) the core of the normalised deviations scattered at up to 1.8x its
stated variance in the weak and middle bins and at 0.1-0.7x in the strongest. Reproduced on
synthetic samples with a known model (a 1.3 read as 1.12, ISa 33 read as 31).
Now (ErrorModel.h/.cpp, host-only, so the GPU and CPU paths share it):
- bins are equal counts in counting I/sigma (I2/s2), where b is identified;
- each bin is calibrated on the median of dev2/var with var from the previous iteration, iterated
to a fixed point - heterogeneity inside a bin no longer biases it, and the median keeps it robust
to tails;
- s2 is the counting variance the merge actually applies the model to (rebuilt at the reflection's
mean), not the observation's own sigma^2.
The separate 6-sigma misfit refit is gone: the median does not need it.
A mean-based fit (misfits cut at z^2 > 2 ln N) was tried first: it calibrates the total variance
best (median rms log chi2 over the 28 sets 0.14 vs 0.19 here) but on heavy-tailed data it sizes
the sigmas on the tails, the merge's outlier test widens with them, and CC1/2 fell 0.80 -> 0.71 on
a powder-contaminated set (0.83 with this fit). Rejected for that.
Offline, 28 sets: rms log chi2 of the median normalised deviation over (counting I/sigma x
resolution) 0.208 -> 0.139 (better on 23), of the mean 0.239 -> 0.191 (better on 22).
Battery, 45 of 48 sets against the 9b6736 run (3 lost to CUDA OOM from GPU contention): space group
unchanged on all; d_min unchanged except two poor multi-lattice sets (1.69 -> 1.56, 1.96 -> 1.90);
ISa x1.13 (median), in-house ISa/XDS 0.73 -> 0.93; ISa*R_meas_lo/0.8 0.93 -> 1.05 (XDS ~1.2);
CC1/2 over the XDS range +0.002 (mean; up 0.014-0.031 on the three poorest sets, else +-0.0001);
CC_model +0.0011, R_model_shell_scaled -0.0007 (mean over 17 open sets); CC_anom +0.003 (mean).
Six private sets: space group, d_min and CC1/2 unchanged, ISa up by 14-67% towards XDS's.
Remaining misfit, not addressed: the excess variance grows slower than <I>^2 (the effective
fractional error falls 2-2.5x from counting I/sigma 5 to 200), so the strongest reflections still
scatter below their sigma on open sets. A third, linear term (as in Aimless) fits it better on most
sets but leaves b unidentified on some (b -> 0 on 4 of 28); not landed.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01D1G8gJVAy6gp1K5Dz3NE5C
