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I've been steadfastly refusing to get myself dragged in this time, but with this very sensible statement (which I am largely in agreement with), I thought I'd throw in one thought, just to stir the pot a little more.
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<div class="">This is not a new idea, but I think it is the most sensible strategy I've heard proposed, and addresses Marin's concerns in a more conventional way. What we are talking about here is the statistical noise present in the FSC curves themselves.
Viewed from the framework of traditional error analysis and propagation of uncertainties, which pretty much every scientist should be familiar with since high-school, (and thus would not be confusing to the non statisticians) the 'correct' solution to this
issue is not to adjust the threshold, but to present FSC curves with error bars. </div>
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<div class="">One can then use a fixed threshold at a level based on expectation values, and simply produce a resolution value which also has an associated uncertainty. This is much better than using a variable threshold and still producing a single number
with no uncertainty estimate! Not only does this approach account for the statistical noise in the FSC curve, but it also should stop people from reporting resolutions as 2.3397 Å, as it would be silly to say 2.3397 +- 0.2. </div>
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<div class="">The cross terms are not ignored, but are used in the production of the error bars. This is a very simple approach, which is certainly closer to being correct than the fixed threshold without error-bars approach, and it solves many of the issues
we have with resolution reporting people do. Of course we still have people who will insist that 3.2+-0.2 is better than 3.3+-0.2, but there isn't much you can do about them... (other than beat them over the head with a statistics textbook).</div>
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<div class="">The caveat, of course, is that like all propagation of uncertainty that it is a linear approximation, and the correlation axis isn't linear, so the typical Normal distributions with linear propagation used to justify propagation of uncertainty
aren't _strictly_ true. However, the approximation is fine as long as the error bars are reasonably small compared to the -1 to 1 range of the correlation axis. Each individual error bar is computed around its expectation value, so the overall nonlinearity
of the correlation isn't a concern.</div>
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<font face="Courier" class=""><span style="font-size: 14px;" class="">--------------------------------------------------------------------------------------<br class="">
Steven Ludtke, Ph.D. <<a href="mailto:sludtke@bcm.edu" class="">sludtke@bcm.edu</a>> Baylor College of Medicine <br class="">
Charles C. Bell Jr., Professor of Structural Biology<br class="">
Dept. of Biochemistry and Molecular Biology (<a href="http://www.bcm.edu/biochem" class="">www.bcm.edu/biochem</a>)<br class="">
Academic Director, CryoEM Core (<a href="http://cryoem.bcm.edu" class="">cryoem.bcm.edu</a>)<br class="">
Co-Director CIBR Center (<a href="http://www.bcm.edu/research/cibr" class="">www.bcm.edu/research/cibr</a>)<br class="">
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<div class="">On Feb 21, 2020, at 10:34 AM, Alexis Rohou <<a href="mailto:a.rohou@gmail.com" class="">a.rohou@gmail.com</a>> wrote:</div>
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This email is not from a BCM Source. Only click links or open attachments you know are safe.</b></font><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class=""></span>
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Hi all,
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<div class="">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: </div>
<div class=""><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_pipermail_3dem_2015-2DAugust_003939.html&d=DwMFaQ&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUCMENrXjn3JLSwlIU6Zmp_JYnRrXesjtsM1u2E&s=CZ3YcAV1LVKXsLT0KjCIRby6j3XPA6GqZcOVP3nMyK0&e=" class="">https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html</a><br class="">
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<div class=""><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_pipermail_3dem_2015-2DAugust_003944.html&d=DwMFaQ&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUCMENrXjn3JLSwlIU6Zmp_JYnRrXesjtsM1u2E&s=oG6lGnei74jC5VVGsfFAdiTpIxrZhs_IH2mH0re5QRM&e=" class="">https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html</a></div>
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<div class="">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.</div>
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<div class="">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.</div>
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<div class="">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.</div>
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<div class="">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.</div>
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<div class="">Hope this helps,</div>
<div class="">Alexis </div>
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<div dir="ltr" class="gmail_attr">On Sun, Feb 16, 2020 at 9:00 AM Penczek, Pawel A <<a href="mailto:Pawel.A.Penczek@uth.tmc.edu" class="">Pawel.A.Penczek@uth.tmc.edu</a>> wrote:<br class="">
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<div dir="auto" class="">Marin,
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<div class="">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. <br class="">
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<div dir="ltr" class="">Regards,
<div class="">Pawel</div>
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<blockquote type="cite" class="">On Feb 16, 2020, at 10:38 AM, Marin van Heel <<a href="mailto:marin.vanheel@googlemail.com" target="_blank" class="">marin.vanheel@googlemail.com</a>> wrote:<br class="">
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<p class=""><font color="Red" size="3" face="arial, sans-serif" class=""><strong class="">**** EXTERNAL EMAIL ****</strong></font></p>
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<div class="">Dear Pawel and All others ....
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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...). <span class=""></span></p>
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<div class="">Sorry</div>
<div class="">Marin<br class="">
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<div dir="ltr" class="gmail_attr">On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A <<a href="mailto:Pawel.A.Penczek@uth.tmc.edu" target="_blank" class="">Pawel.A.Penczek@uth.tmc.edu</a>> wrote:<br class="">
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<div dir="ltr" class="">Dear Teige,
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<div class="">I am wondering whether you are familiar with</div>
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Resolution measures in molecular electron microscopy.</h2>
<div id="gmail-m_-325618919662780292gmail-m_4473107327319981263gmail-m_-4642610284911275282cit_summary" style="box-sizing: border-box; font-size: 14px; color: rgb(39, 39, 39); font-family: Arial;" class="">
<div style="box-sizing: border-box;" class="">Penczek PA. Methods Enzymol. 2010.</div>
</div>
<div id="gmail-m_-325618919662780292gmail-m_4473107327319981263gmail-m_-4642610284911275282cit_full" style="box-sizing: border-box; font-size: 14px; color: rgb(39, 39, 39); font-family: Arial;" class="">
<h3 style="box-sizing: border-box; font-family: "Lucida Grande", "Helvetica Neue", Helvetica, Arial; margin-bottom: 0px; font-size: 14px;" class="">
Citation</h3>
<p style="box-sizing: border-box; margin: 2px 0px;" class="">Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8.</p>
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<div class="">You will find there answers to all questions you asked and much more. </div>
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<div dir="ltr" class="">Regards,
<div class="">Pawel Penczek</div>
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<br class="">
<br class="">
<div dir="ltr" class="">Regards,
<div class="">Pawel</div>
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