[3dem] Which resolution?

[Alexis Rohou]

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 <
Pawel.A.Penczek at uth.tmc.edu> 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 <marin.vanheel at googlemail.com>
> 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 <
> Pawel.A.Penczek at uth.tmc.edu> 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
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