How a seemingly innocent question can explode ...
I actually thought I understood this but little of what has been
discussed matches my "mental picture" of the truncate process.
Truncate can do multiple things, but the truncate part I believe really
just deals with converting I to F and the inherent problems due to
experimental error and mathematical problems in deriving SigF from SigI
when I is near zero. This only depends on how close I is to zero
(relative to SigI), and not on the Wilson distribution itself.
My mental picture is as follows:
Visualize a gaussian distribution representing I and its standard
deviation, with I being close to zero (either positive or negative).
Part of the gaussian will stretch into negative-I territory, which is
fine for the experimental I (because of experimental error) but not the
true I. Given this prior knowledge you can re-estimate I by TRUNCATEing
the negative tail of the gaussian and integrating just the positive part
to find the new mean and standard deviation. As a result any reflection
will become positive (including those starting out with negative I). The
extend to which the method affects the intensity depends on how much of
a negative tail it has, so nearly no effect on I/SigI>=2 reflections and
not really that much on even I/SigI=2 reflections.
I actually think this is a very elegant solution. The only thing better,
is to use I directly and avoid the entire issue. I personally think you
want to use the experimental I without correcting it as explained above
since it will introduce bias and the refinement procedure should take
proper care of random experimental error, unless you mess around with
it. However, when you need amplitudes, truncate is the way to go.
Bart
Ian Tickle wrote:
> But there's a fundamental difference in approach, the authors here
> assume the apparently simpler prior distribution P(I) = 0 for I < 0 &
> P(I) = const for I >= 0. As users of Bayesian priors well know this is
> an improper prior since it integrates to infinity instead of unity.
> This means that, unlike the case I described for the French & Wilson
> formula based on the Wilson distribution which gives unbiased estimates
> of the true I's and their average, the effect on the corrected
> intensities of using this prior really will be to increase all
> intensities (since the mean I for this prior PDF is also infinite!),
> hence the intensities and their average must be biased (& I'm sure the
> same goes for the corresponding F's). But as you say in practice the
> errors introduced may well not be significant compared with those
> introduced by (for example) deconvoluting the overlapping peaks in the
> powder pattern. Also I'm not sure the F vs I argument can be carried
> over from the powder to the single crystal case because the kinds of
> errors encountered in each case are quite different.
>
> -- Ian
>
>
>>-----Original Message-----
>>From: [log in to unmask]
>>[mailto:[log in to unmask]] On Behalf Of [log in to unmask]
>>Sent: 08 September 2008 22:20
>>To: Jacob Keller
>>Cc: [log in to unmask]
>>Subject: Re: [ccp4bb] truncate ignorance
>>
>>I would also recommend reading of the following paper:
>>
>>D.S. Sivia & W.I.F. David (1994), Acta Cryst. A50, 703-714. A
>>Bayesian
>>Approach to Extracting Structure-Factor Amplitudes from Powder
>>Diffraction Data.
>>
>>Despite of the title, most of the analysis presented in this paper
>>applies equally well to single-crystal data (see especially
>>sections 3
>>and 5). If you are not interested in the specific powder-diffraction
>>problems (i.e. overlapping peaks), you can simply skip
>>sections 4 and 6.
>>
>>A few interesting points from this paper :
>>
>>(1) The conversion from I's to F's can be done (in a Bayesian
>>way) by
>>applying two simple formula (equations 11 and 12 in the
>>paper), which,
>>for all practical purposes, are as valid as the more complicated
>>French & Wilson procedure (see discussion in section 5).
>>
>>(2) Re. the use of I's rather than F's : this is discussed on
>>page 710
>>(final part of section 5). The authors seem to be more in favor of
>>using F's.
>>
>>
>>
>>Marc Schiltz
>>
>>
>>
>>
>>
>>Quoting Jacob Keller <[log in to unmask]>:
>>
>>
>>>Does somebody have a .pdf of that French and Wilson paper?
>>>
>>>Thanks in advance,
>>>
>>>Jacob
>>>
>>>*******************************************
>>>Jacob Pearson Keller
>>>Northwestern University
>>>Medical Scientist Training Program
>>>Dallos Laboratory
>>>F. Searle 1-240
>>>2240 Campus Drive
>>>Evanston IL 60208
>>>lab: 847.491.2438
>>>cel: 773.608.9185
>>>email: [log in to unmask]
>>>*******************************************
>>>
>>>----- Original Message -----
>>>From: "Ethan Merritt" <[log in to unmask]>
>>>To: <[log in to unmask]>
>>>Sent: Monday, September 08, 2008 3:03 PM
>>>Subject: Re: [ccp4bb] truncate ignorance
>>>
>>>
>>>
>>>>On Monday 08 September 2008 12:30:29 Phoebe Rice wrote:
>>>>
>>>>>Dear Experts,
>>>>>
>>>>>At the risk of exposing excess ignorance, truncate makes me
>>>>>very nervous because I don't quite get exactly what it is
>>>>>doing with my data and what its assumptions are.
>>>>>
>>>>>From the documentation:
>>>>>========================================================
>>>>>... the "truncate" procedure (keyword TRUNCATE YES, the
>>>>>default) calculates a best estimate of F from I, sd(I), and
>>>>>the distribution of intensities in resolution shells (see
>>>>>below). This has the effect of forcing all negative
>>>>>observations to be positive, and inflating the weakest
>>>>>reflections (less than about 3 sd), because an observation
>>>>>significantly smaller than the average intensity is likely
>>>>>to be underestimated.
>>>>>=========================================================
>>>>>
>>>>>But is it really true, with data from nice modern detectors,
>>>>>that the weaklings are underestimated?
>>>>
>>>>It isn't really an issue of the detector per se, although in
>>>>principle you could worry about non-linear response to the
>>>>input rate of arriving photons.
>>>>
>>>>In practice the issue, now as it was in 1977 (French&Wilson),
>>>>arises from the background estimation, profile fitting, and
>>>>rescaling that are applied to the individual pixel contents
>>>>before they are bundled up into a nice "Iobs".
>>>>
>>>>I will try to restate the original French & Wilson argument,
>>>>avoiding the terminology of maximum likelihood and
>>
>>Bayesian statistics.
>>
>>>>1) We know the true intensity cannot be negative.
>>>>2) The existence of Iobs<0 reflections in the data set means
>>>> that whatever we are doing is producing some values of
>>>> Iobs that are too low.
>>>>3) Assuming that all weak-ish reflections are being processed
>>>> equivalently, then whatever we doing wrong for reflections with
>>>> Iobs near zero on the negative side surely is also going wrong
>>>> for their neighbors that happen to be near Iobs=0 on the positive
>>>> side.
>>>>4) So if we "correct" the values of Iobs that went negative, for
>>>> consistency we should also correct the values that are nearly
>>>> the same but didn't quite tip over into the negative range.
>>>>
>>>>
>>>>>Do I really want to inflate them?
>>>>
>>>>Yes.
>>>>
>>>>
>>>>>Exactly what assumptions is it making about the expected
>>>>>distributions?
>>>>
>>>>Primarily that
>>>>1) The histogram of true Iobs is smooth
>>>>2) No true Iobs are negative
>>>>
>>>>
>>>>>How compatible are those assumptions with serious anisotropy
>>>>>and the wierd Wilson plots that nucleic acids give?
>>>>
>>>>Not relevant
>>>>
>>>>
>>>>>Note the original 1978 French and Wilson paper says:
>>>>>"It is nevertheless important to validate this agreement for
>>>>>each set of data independently, as the presence of atoms in
>>>>>special positions or the existence of noncrystallographic
>>>>>elements of symmetry (or pseudosymmetry) may abrogate the
>>>>>application of these prior beliefs for some crystal
>>>>>structures."
>>>>
>>>>It is true that such things matter when you get down to the
>>>>nitty-gritty details of what to use as the "expected distribution".
>>>>But *all* plausible expected distributions will be non-negative
>>>>and smooth.
>>>>
>>>>
>>>>
>>>>>Please help truncate my ignorance ...
>>>>>
>>>>> Phoebe
>>>>>
>>>>>==========================================================
>>>>>Phoebe A. Rice
>>>>>Assoc. Prof., Dept. of Biochemistry & Molecular Biology
>>>>>The University of Chicago
>>>>>phone 773 834 1723
>>>>>
>>
>>http://bmb.bsd.uchicago.edu/Faculty_and_Research/01_Faculty/01
>>_Faculty_Alphabetically.php?faculty_id=123
>>
>>>>>RNA is really nifty
>>>>>DNA is over fifty
>>>>>We have put them
>>>>> both in one book
>>>>>Please do take a
>>>>> really good look
>>>>>http://www.rsc.org/shop/books/2008/9780854042722.asp
>>>>>
>>>>
>>>>
>>>>
>>>>--
>>>>Ethan A Merritt
>>>>Biomolecular Structure Center
>>>>University of Washington, Seattle 98195-7742
>>>>
>>>
>>
>
>
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--
Bart Hazes (Associate Professor)
Dept. of Medical Microbiology & Immunology
University of Alberta
1-15 Medical Sciences Building
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Canada, T6G 2H7
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