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://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html
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 < [email protected]> 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 <[email protected]> > 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 < > [email protected]> 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 >> [email protected] >> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem >> <https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_mailman_listinfo_3dem&d=DwMFaQ&c=bKRySV-ouEg_AT-w2QWsTdd9X__KYh9Eq2fdmQDVZgw&r=yEYHb4SF2vvMq3W-iluu41LlHcFadz4Ekzr3_bT4-qI&m=3-TZcohYbZGHCQ7azF9_fgEJmssbBksaI7ESb0VIk1Y&s=XHMq9Q6Zwa69NL8kzFbmaLmZA9M33U01tBE6iAtQ140&e=> >> > _______________________________________________ > 3dem mailing list > [email protected] > https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem > ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
