This example is based on real (electron microscopy) data and shows the importance of having reasonably accurate estimates of the errors present in the data. The left-hand-side panel on the figure that follows is the conventional 30Å projection of photosystem II (courtesy Dr Andreas Holzenburg). The other three panels show GraphEnt maps which were calculated with standard deviations ranging from grossly overestimated (second from the left) to seriously underestimated (right hand side panel). Clearly, overestimating the standard deviations is no harm : although the final map will not be the best that can be done with the data, it will not be possible to misinterpret it. Underestimating the standard deviations, on the other hand, can lead to serious problems : the MAXENT algorithm will be ``fitting'' noise instead of real signal and the final map will contain fine structure not required by the data. Misinterpreting such a GraphEnt map should present no problems.
It is worth mentioning on passing that most data processing programs will produce raw data with underestimated standard deviations (especially for weak reflections). The solution is, of course, to calculate a normal probability plot of the form (Iobs - < I > )/
(I) and
confirm that it has mean 0 and variance 1.
I should also mention here that the greatest problem with incorrectly
estimated standard deviations appears to come from the electron microscopy
field : the majority of the data sets that I have come across tend to have
almost constant average values of
F/(F) throughout the resolution
range. An example of what GraphEnt would do in such cases is presented in
section 9.8.
