I would think the most information-reflecting representation for systematic absences (or maybe for all reflections) would be not I/sig but the reflection's (|log|) ratio to the expected intensity in that shell (median intensity, say). Thus, when the median intensity is 1000 counts, and one observes a spot of 1 count, this would be quite information-rich even though its I/sig would be really small.
This approach would also reflect the lesser information contained in twinned data, where deviations from mean intensities are smaller, even though I/sig be quite large.
Regarding spots that are not systematic absence candidates, isn't it true that a very weak spot (e.g. 10 counts) of I/sig = 2 might contain more information than a strong spot (1000 counts) of I/sig = 20 in the same shell, if the median counts in the shell were 1000?
I used to hear rumors that maps calculated from the 1000 strongest spots were almost tantamount to using all reflections; maybe these flaky maps would be improved by using instead the 1000 reflections which deviate most from expected intensities? (i.e., both stronger and weaker.)
Maybe more generally, should refinement incorporate weighting for these deviant spots? Or maybe it already does, but my understanding was that I/sig was the most salient for weighting.
I guess the general idea is that the more unexpected the value is, the more it captures something unique about the thing being measured, thus more information.
JPK
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-----Original Message-----
From: CCP4 bulletin board <[log in to unmask]> On Behalf Of Kay Diederichs
Sent: Tuesday, March 10, 2020 2:48 AM
To: [log in to unmask]
Subject: Re: [ccp4bb] [3dem] Which resolution?
I'd say that it depends on your state of knowledge, and on their I and sigma.
- if you know the space group for sure before you do the measurement of the systematic absences, their I and sigma don't matter to you (because they don't influence your mental model of the experiment), so their information content is (close to) zero.
- if the space group is completely unknown, some groups of reflections (e.g. h,k,l = 0,0,2n+1) can only be considered "potentially systematic absences". Then both I and sigma matter. "small" or "high" I/sigma for each member of such a group of reflections would indeed add quite some information in this situation, so an information content of up to 1 bit would be justified. "intermediate" I/sigma (say, 0.5 to 2) would be closer to zero bit, since it does not let you safely decide between "yes" or "no" (the recent paper by Randy Read and coworkers relates I and sigma to bits of information, but not in the context of decision making from potentially systematic absent reflections).
So it is not quite straightforward, I think.
best wishes,
Kay
On Tue, 10 Mar 2020 01:26:03 +0100, James Holton <[log in to unmask]> wrote:
>I'd say they are 1 bit each, since they are the answer to a yes-or-no
>question.
>
>-James Holton
>MAD Scientist
>
>On 2/27/2020 6:32 PM, Keller, Jacob wrote:
>> How would one evaluate the information content of systematic absences?
>>
>> JPK
>>
>> On Feb 26, 2020 8:14 PM, James Holton <[log in to unmask]> wrote:
>> In my opinion the threshold should be zero bits. Yes, this is where
>> CC1/2 = 0 (or FSC = 0). If there is correlation then there is
>> information, and why throw out information if there is information to
>> be had? Yes, this information comes with noise attached, but that is
>> why we have weights.
>>
>> It is also important to remember that zero intensity is still useful
>> information. Systematic absences are an excellent example. They
>> have no intensity at all, but they speak volumes about the structure.
>> In a similar way, high-angle zero-intensity observations also tell us
>> something. Ever tried unrestrained B factor refinement at poor
>> resolution? It is hard to do nowadays because of all the safety
>> catches in modern software, but you can get great R factors this way.
>> A telltale sign of this kind of "over fitting" is remarkably large
>> Fcalc values beyond the resolution cutoff. These don't contribute to
>> the R factor, however, because Fobs is missing for these hkls. So,
>> including zero-intensity data suppresses at least some types of
>> over-fitting.
>>
>> The thing I like most about the zero-information resolution cutoff is
>> that it forces us to address the real problem: what do you mean by
>> "resolution" ? Not long ago, claiming your resolution was 3.0 A
>> meant that after discarding all spots with individual I/sigI < 3 you
>> still have 80% completeness in the 3.0 A bin. Now we are saying we
>> have a
>> 3.0 A data set when we can prove statistically that a few
>> non-background counts fell into the sum of all spot areas at 3.0 A.
>> These are not the same thing.
>>
>> Don't get me wrong, including the weak high-resolution information
>> makes the model better, and indeed I am even advocating including all
>> the noisy zeroes. However, weak data at 3.0 A is never going to be
>> as good as having strong data at 3.0 A. So, how do we decide? I
>> personally think that the resolution assigned to the PDB deposition
>> should remain the classical I/sigI > 3 at 80% rule. This is really
>> the only way to have meaningful comparison of resolution between very
>> old and very new structures. One should, of course, deposit all the
>> data, but don't claim that cut-off as your "resolution". That is
>> just plain unfair to those who came before.
>>
>> Oh yeah, and I also have a session on "interpreting low-resolution
>> maps" at the GRC this year.
>> https://urldefense.com/v3/__https://www.grc.org/diffraction-methods-i
>> n-structural-biology-conference/2020/__;!!Eh6p8Q!XrEJFTzyDh5AKIyF7aqX
>> MswM8g5VF_7U-msuYRN_IWolD5KPaoP8Xsj8THkFrPUFJmw$
>>
>> So, please, let the discussion continue!
>>
>> -James Holton
>> MAD Scientist
>>
>> On 2/22/2020 11:06 AM, Nave, Colin (DLSLtd,RAL,LSCI) wrote:
>>>
>>> Alexis
>>>
>>> This is a very useful summary.
>>>
>>> You say you were not convinced by Marin's derivation in 2005. Are
>>> you convinced now and, if not, why?
>>>
>>> My interest in this is that the FSC with half bit thresholds have
>>> the danger of being adopted elsewhere because they are becoming
>>> standard for protein structure determination (by EM or MX). If it is
>>> used for these mature techniques it must be right!
>>>
>>> It is the adoption of the ½ bit threshold I worry about. I gave a
>>> rather weak example for MX which consisted of partial occupancy of
>>> side chains, substrates etc. For x-ray imaging a wide range of
>>> contrasts can occur and, if you want to see features with only a
>>> small contrast above the surroundings then I think the half bit
>>> threshold would be inappropriate.
>>>
>>> It would be good to see a clear message from the MX and EM
>>> communities as to why an information content threshold of ½ a bit is
>>> generally appropriate for these techniques and an acknowledgement
>>> that this threshold is technique/problem dependent.
>>>
>>> We might then progress from the bronze age to the iron age.
>>>
>>> Regards
>>>
>>> Colin
>>>
>>> *From:*CCP4 bulletin board <[log in to unmask]> *On Behalf Of
>>> *Alexis Rohou
>>> *Sent:* 21 February 2020 16:35
>>> *To:* [log in to unmask]
>>> *Subject:* Re: [ccp4bb] [3dem] Which resolution?
>>>
>>> Hi all,
>>>
>>> For those bewildered by Marin's insistence that everyone's been
>>> messing up their stats since the bronze age, I'd like to offer what
>>> my understanding of the situation. More details in this thread from
>>> a few years ago on the exact same topic:
>>>
>>> https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3d
>>> em/2015-August/003939.html__;!!Eh6p8Q!XrEJFTzyDh5AKIyF7aqXMswM8g5VF_
>>> 7U-msuYRN_IWolD5KPaoP8Xsj8THkFyeegrI8$
>>> <https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3
>>> dem/2015-August/003939.html__;!!Eh6p8Q!TK-tIY-zm5coRu74uWMkIJkTFWNz4
>>> -1ibr1oaahxT_2BAAetUTMNdfRqUCmIsJF61uc$>
>>>
>>> https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3d
>>> em/2015-August/003944.html__;!!Eh6p8Q!XrEJFTzyDh5AKIyF7aqXMswM8g5VF_
>>> 7U-msuYRN_IWolD5KPaoP8Xsj8THkFj5n6OLY$
>>> <https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3
>>> dem/2015-August/003944.html__;!!Eh6p8Q!TK-tIY-zm5coRu74uWMkIJkTFWNz4
>>> -1ibr1oaahxT_2BAAetUTMNdfRqUCmIPu-nRBo$>
>>>
>>> Notwithstanding notational problems (e.g. strict equations as
>>> opposed to approximation symbols, or omission of symbols to denote
>>> estimation), I believe Frank & Al-Ali and "descendent" papers (e.g.
>>> appendix of Rosenthal & Henderson 2003) are fine. The cross terms
>>> that Marin is agitated about indeed do in fact have an expectation
>>> value of 0.0 (in the ensemble; if the experiment were performed an
>>> infinite number of times with different realizations of noise). I
>>> don't believe Pawel or Jose Maria or any of the other authors really
>>> believe that the cross-terms are orthogonal.
>>>
>>> When N (the number of independent Fouier voxels in a shell) is large
>>> enough, mean(Signal x Noise) ~ 0.0 is only an approximation, but a
>>> pretty good one, even for a single FSC experiment. This is why, in
>>> my book, derivations that depend on Frank & Al-Ali are OK, under the
>>> strict assumption that N is large. Numerically, this becomes
>>> apparent when Marin's half-bit criterion is plotted - asymptotically
>>> it has the same behavior as a constant threshold.
>>>
>>> So, is Marin wrong to worry about this? No, I don't think so. There
>>> are indeed cases where the assumption of large N is broken. And
>>> under those circumstances, any fixed threshold (0.143, 0.5,
>>> whatever) is dangerous. This is illustrated in figures of van Heel &
>>> Schatz (2005). Small boxes, high-symmetry, small objects in large
>>> boxes, and a number of other conditions can make fixed thresholds dangerous.
>>>
>>> It would indeed be better to use a non-fixed threshold. So why am I
>>> not using the 1/2-bit criterion in my own work? While numerically it
>>> behaves well at most resolution ranges, I was not convinced by
>>> Marin's derivation in 2005. Philosophically though, I think he's
>>> right - we should aim for FSC thresholds that are more robust to the
>>> kinds of edge cases mentioned above. It would be the right thing to do.
>>>
>>> Hope this helps,
>>>
>>> Alexis
>>>
>>> On Sun, Feb 16, 2020 at 9:00 AM Penczek, Pawel A
>>> <[log in to unmask] <mailto:[log in to unmask]>> wrote:
>>>
>>> Marin,
>>>
>>> The statistics in 2010 review is fine. You may disagree with
>>> assumptions, but I can assure you the “statistics” (as you call
>>> it) is fine. Careful reading of the paper would reveal to you
>>> this much.
>>>
>>> Regards,
>>>
>>> Pawel
>>>
>>>
>>>
>>> On Feb 16, 2020, at 10:38 AM, Marin van Heel
>>> <[log in to unmask]
>>> <mailto:[log in to unmask]>> wrote:
>>>
>>>
>>>
>>> ***** EXTERNAL EMAIL *****
>>>
>>> Dear Pawel and All others ....
>>>
>>> This 2010 review is - unfortunately - largely based on the
>>> flawed statistics I mentioned before, namely on the a priori
>>> assumption that the inner product of a signal vector and a
>>> noise vector are ZERO (an orthogonality assumption). The
>>> (Frank & Al-Ali 1975) paper we have refuted on a number of
>>> occasions (for example in 2005, and most recently in our
>>> BioRxiv paper) but you still take that as the correct
>>> relation between SNR and FRC (and you never cite the
>>> criticism...).
>>>
>>> Sorry
>>>
>>> Marin
>>>
>>> On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A
>>> <[log in to unmask]
>>> <mailto:[log in to unmask]>> wrote:
>>>
>>> Dear Teige,
>>>
>>> I am wondering whether you are familiar with
>>>
>>>
>>> Resolution measures in molecular electron microscopy.
>>>
>>> Penczek PA. Methods Enzymol. 2010.
>>>
>>>
>>> Citation
>>>
>>> Methods Enzymol. 2010;482:73-100. doi:
>>> 10.1016/S0076-6879(10)82003-8.
>>>
>>> You will find there answers to all questions you asked
>>> and much more.
>>>
>>> Regards,
>>>
>>> Pawel Penczek
>>>
>>> Regards,
>>>
>>> Pawel
>>>
>>> _______________________________________________
>>> 3dem mailing list
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