On Friday, 23 January, 2015 20:36:08 Keller, Jacob wrote:
> No wikipedia link yet?
In practice the issue usually comes down to a consideration of the noise.
Is the noise systematic? Is the signal/noise constant over time?
If the noise is systematic, then repeated measurement of the same
data points will be biased by that systematic factor and will
overestimate the accuracy of the data. This is an example of when
precision is distinct from accuracy. On the other hand this
protocol may allow you to better estimate and correct for a decrease
in signal/noise as a function of time.
Conversely spreading the measurement effort over a larger number
of points may result in a larger apparent sigma (lower precision)
but greater accuracy overall since the systematic effects are
more likely to be correctly identified as noise.
Relating this back to fine-slicing on phi, if the noise has a large
per-image component then fine-slicing is a bad idea because you
increase the noise for no gain in signal. On the other hand if
there is little or no per-image noise component, as is the case
for photon counting detectors, then fine-slicing potentially
decreases the noise because you do not have to estimate and subtract
the background from the portion of the time the reflection of
interest does not intersect the Ewald sphere.
Ethan
>
> JPK
>
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Keller,
> Jacob
> Sent: Thursday, January 22, 2015 5:20 PM
> To: CCP4BB@JISCMAIL.AC.UK
> Subject: [ccp4bb] Continuous-Single Versus Coarse-Multiple Sampling
>
> Dear Crystallographers,
>
> This is more general than crystallography, but has applications therein,
> particularly in understanding fine phi-slicing.
>
> The general question is:
>
> Given one needs to collect data to fit parameters for a known function, and
> given a limited total number of measurements, is it generally better to
> measure a small group of points multiple times or to distribute each
> individual measurement over the measureable extent of the function? I have a
> strong intuition that it is the latter, but all errors being equal, it would
> seem prima facie that both are equivalent. For example, a line (y = mx + b)
> can be fit from two points. One could either measure the line at two points A
> and B five times each for a total of 10 independent measurements, or measure
> ten points evenly-spaced from A to B. Are these equivalent in terms of
> fitting and information content or not? Which is better? Again, conjecture
> and intuition suggest the evenly-spaced experiment is better, but I cannot
> formulate or prove to myself why, yet.
>
> The application of this to crystallography might be another reason that fine
> phi-slicing (0.1 degrees * 3600 frames) is better than coarse (1 degree *
> 3600 frames), even though the number of times one measures reflections is
> tenfold higher in the second case (assuming no radiation damage). In the
> first case, one never measures the same phi angle twice, but one does have
> multiple measurements in a sense, i.e., of different parts of the same
> reflection.
>
> Yes, 3D profile-fitting may be a big reason fine phi-slicing works, but
> beyond that, perhaps this sampling choice plays a role as well. Or maybe the
> profile-fitting works so well precisely because of this diffuse-single type
> of sampling rather than coarse-multiple sampling?
>
> This general math/science concept must have been discussed somewhere--can
> anyone point to where?
>
> JPK
>
> *******************************************
> Jacob Pearson Keller, PhD
> Looger Lab/HHMI Janelia Research Campus
> 19700 Helix Dr, Ashburn, VA 20147
> email: kell...@janelia.hhmi.org
> *******************************************
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
MS 357742, University of Washington, Seattle 98195-7742
