Hi Ian,
The initial question was about which procedures to convert intensities
to amplitudes are deemed acceptable. I was proposing the Sivia & David
(1994) method as an alternative to the French & Wilson (1978) method.
You were objecting against this and came up with data simulations which
were intended to demonstrate the inferiority of the S&D method. I
continue to think that your simulations do not in any way substantiate
this claim because I think that you are overly concerned by the bias of
the averages (or the average bias). This is the criterion which you use
to judge that one method is better than another. I doubt that this is
pertinent and I think that one can not simply use the average bias to
appraise various truncate methods.
I repeat my previous proposal : implement a new truncate procedure,
where the intensities of all reflections are simply set equal to their
shell averages (a procedure which no one would seriously consider, but
which yields zero average bias - the quantity which you are so concerned
about).
I still find it difficult to understand what exactly it is that you are
calculating in your simulated data. Because you are now stating that you
are "certainly not averaging over reflections". If this is so, then I am
starting to wonder what all our previous discussions were about ? But in
any event, I propose you to implement the truncate procedure mentioned
above, i.e. where you set the corrected intensities simply equal to S
(the Wilson distribution parameter - assumed to be known), run your data
simulation and send us the statistics. We can then discuss the merits of
these statistics in deciding what should be the best truncate procedure.
There are many other points in your mail which would deserve a more
thorough discussion, but I am not sure whether the BB is still the right
place for this (I doubt that anyone else out there is still following
our e-mail exchange), but I feel that I must pick up this one comment
you made in response to my earlier message :
I'm rather puzzled that you say:
The F&W procedure completely distorts the second moment about the
mean of the intensity distributions. For weak data it is close to 0,
whereas the true second moment about the mean of the distribution
is 1.0. Now, I would find this much more worrisome than a slightly
distorted shell average.
Surely the effect of including prior information is invariably to reduce
the uncertainties of the derived parameters, often drastically? - and
doesn't a reduced uncertainty or RMS error represent an improvement?
It seems to me that you are thinking about Truncate as a method for
estimating S, and therefore consider it beneficial if the RMS error on
the "parameter" S is reduced. Is this really what you think ?
Best regards
Marc
--
Marc SCHILTZ http://lcr.epfl.ch
