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<p>I support this idea of computing error bars, and we may think to
compute "horizontal" error bars, rather than "vertical" ones. That
is, the (horizontal) error bar of the reported resolution (when it
crosses several thresholds). In a way, that was explored in Fig. 2
of the BlocRes paper (<a
href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3837392/">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3837392/</a>),
although the representation was not as error bars, there was no
multiple subsets, and the resolution was measured locally instead
lof globally. But, what was clear was that the variability at low
thresholds and high resolution, could be very unstable, which is
also our experience.</p>
<p>Kind regards, Carlos Oscar<br>
</p>
<div class="moz-cite-prefix">El 22/02/2020 a las 15:49, Ludtke,
Steven J. escribió:<br>
</div>
<blockquote type="cite"
cite="mid:ED84AA45-0089-49C8-BC12-3C962BA4E843@bcm.edu">
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Hi Jose-Maria,
<div class="">I completely agree that the error bars are going to
be small in the typical large data set at high resolution that
we're dealing with today. That's exactly as it should be. </div>
<div class=""><br class="">
</div>
<div class="">However, two counterpoints: </div>
<div class="">1) with the rise of in-situ subtomogram averaging,
many data sets and volume sizes are going to be smaller again,
at least for a while. </div>
<div class=""><br class="">
</div>
<div class="">2) even if the error bars are small, they give a
basis for producing an uncertainty value on the resolution,
which I think is something we really need to help combat the
people going to extreme lengths (and screwing up their maps) to
get a completely meaningless 0.05 Å resolution 'improvement"</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
<div class="">
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<font class="" face="Courier"><span style="font-size:
14px;" class="">--------------------------------------------------------------------------------------<br
class="">
Steven Ludtke, Ph.D. <<a
href="mailto:sludtke@bcm.edu" class=""
moz-do-not-send="true">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=""
moz-do-not-send="true">www.bcm.edu/biochem</a>)<br
class="">
Academic Director, CryoEM Core
(<a
href="http://cryoem.bcm.edu" class=""
moz-do-not-send="true">cryoem.bcm.edu</a>)<br
class="">
Co-Director CIBR Center
(<a
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moz-do-not-send="true">www.bcm.edu/research/cibr</a>)<br
class="">
<br class="">
</span></font><br class="">
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<div><br class="">
<blockquote type="cite" class="">
<div class="">On Feb 22, 2020, at 3:19 AM, Jose Maria Carazo
<<a href="mailto:carazo@cnb.csic.es" class=""
moz-do-not-send="true">carazo@cnb.csic.es</a>> wrote:</div>
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Dear Chuck, so nice to here from you!
<div class=""><br class="">
</div>
<div class="">Yes, the idea of having error bars (to
have a minimal understading of the distribution of
FSC's characterizing your map) is very appealing......
the problem is that every ad hoc attempt we have done
in that respect has given us very low spread for large
data sets. I am sure it can be done better, and that
in some cases it may be of value, but all seemed to be
quite a lot of work if you wanted to do it well, with
not so great prospects (on the other hand, now that
algorithms go so fast, perhaps simple resampling
strategies would be worth to be explored to re.check
if really the spread is small)</div>
<div class=""><br class="">
</div>
<div class="">Wbw..JM</div>
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<div dir="ltr" class="gmail_attr">On Fri, Feb 21, 2020
at 8:56 PM Sindelar, Charles <<a
href="mailto:charles.sindelar@yale.edu" class=""
moz-do-not-send="true">charles.sindelar@yale.edu</a>>
wrote:<br class="">
</div>
<blockquote class="gmail_quote" style="margin: 0px 0px
0px 0.8ex; border-left-width: 1px; border-left-style:
solid; border-left-color: rgb(204, 204, 204);
padding-left: 1ex;">
Hear! Hear! To Alexis and Steve's points- I think
these concisely capture the reason why most of us
(myself included) are content to use the widely
accepted 0.143 criterion- bearing in mind the
important caveats that have been raised.<br class="">
<br class="">
One way to summarize the difference between the "0.143
threshold" approach and the "half-bit" approach (van
Heel & Schatz (2005)) is that they attempt answer
different questions-<span
class="Apple-converted-space"> </span><br class="">
<br class="">
(1) What is a minimally biased estimate of the
resolution. (0.143)<br class="">
<br class="">
vs<br class="">
<br class="">
(2) What is the highest resolution one can
confidently claim one has. (half-bit)<br class="">
<br class="">
The second approach suffers from the problem that as
the noise in the measurement increasesa resampling
approac, there is a systematic bias to underestimate
the resolution (and who wants to do that??). Plus, I
enjoy the whimsy of rallying around a seemingly
arbitrary number ("0.143").<br class="">
<br class="">
To improve the statistics, one could compute a large
number of gold-standard FSC curves from resampled
subsets of the data. But that hardly seems worth it
when the bigger problems often come from other sources
of systematic error, as many have noted. I like
Steve's idea of reporting error bars on the resolution
estimate.<br class="">
<br class="">
- Chuck<br class="">
<br class="">
<br class="">
Today's Topics:<br class="">
<br class="">
1. Re: Which resolution? (Alexis Rohou)<br
class="">
2. Re: Which resolution? (Ludtke, Steven J.)<br
class="">
<br class="">
<br class="">
----------------------------------------------------------------------<br
class="">
<br class="">
Message: 1<br class="">
Date: Fri, 21 Feb 2020 08:34:45 -0800<br class="">
From: Alexis Rohou <<a
href="mailto:a.rohou@gmail.com" target="_blank"
class="" moz-do-not-send="true">a.rohou@gmail.com</a>><br
class="">
To: "Penczek, Pawel A" <<a
href="mailto:Pawel.A.Penczek@uth.tmc.edu"
target="_blank" class="" moz-do-not-send="true">Pawel.A.Penczek@uth.tmc.edu</a>><br
class="">
Cc: "<a href="mailto:3dem@ncmir.ucsd.edu"
target="_blank" class="" moz-do-not-send="true">3dem@ncmir.ucsd.edu</a>"
<<a href="mailto:3dem@ncmir.ucsd.edu"
target="_blank" class="" moz-do-not-send="true">3dem@ncmir.ucsd.edu</a>>,
Marin van Heel<br class="">
<<a
href="mailto:marin.vanheel@googlemail.com"
target="_blank" class="" moz-do-not-send="true">marin.vanheel@googlemail.com</a>>,
"<a href="mailto:ccpem@jiscmail.ac.uk" target="_blank"
class="" moz-do-not-send="true">ccpem@jiscmail.ac.uk</a>"<br
class="">
<<a href="mailto:ccpem@jiscmail.ac.uk"
target="_blank" class="" moz-do-not-send="true">ccpem@jiscmail.ac.uk</a>>,
"<a href="mailto:CCP4BB@JISCMAIL.AC.UK"
target="_blank" class="" moz-do-not-send="true">CCP4BB@JISCMAIL.AC.UK</a>"<br
class="">
<<a href="mailto:CCP4BB@jiscmail.ac.uk"
target="_blank" class="" moz-do-not-send="true">CCP4BB@jiscmail.ac.uk</a>><br
class="">
Subject: Re: [3dem] Which resolution?<br class="">
Message-ID:<br class="">
<<a
href="mailto:CAM5goXS5xK2OoBUSFDQzv7HgnkiGw6nZSU0%2BA5BJoKVcT20o_A@mail.gmail.com"
target="_blank" class="" moz-do-not-send="true">CAM5goXS5xK2OoBUSFDQzv7HgnkiGw6nZSU0+A5BJoKVcT20o_A@mail.gmail.com</a>><br
class="">
Content-Type: text/plain; charset="utf-8"<br
class="">
<br class="">
Hi all,<br class="">
<br class="">
For those bewildered by Marin's insistence that
everyone's been messing up<br class="">
their stats since the bronze age, I'd like to
offer what my understanding<br class="">
of the situation. More details in this thread from
a few years ago on the<br class="">
exact same topic:<br 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=xmaCSRNPE3u67PDAef4f-xpFdDA-9JanE7OO-BicWjE&s=o3kcrNwzvjqKQXAYVB7CWUcF2U6kQrfnuV6keMXervs&e="
rel="noreferrer" target="_blank" class=""
moz-do-not-send="true">https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html</a><br
class="">
<br class="">
Notwithstanding notational problems (e.g. strict
equations as opposed to<br class="">
approximation symbols, or omission of symbols to
denote estimation), I<br class="">
believe Frank & Al-Ali and "descendent" papers
(e.g. appendix of Rosenthal<br class="">
& Henderson 2003) are fine. The cross terms
that Marin is agitated about<br class="">
indeed do in fact have an expectation value of 0.0
(in the ensemble; if the<br class="">
experiment were performed an infinite number of
times with different<br class="">
realizations of noise). I don't believe Pawel or
Jose Maria or any of the<br class="">
other authors really believe that the cross-terms
are orthogonal.<br class="">
<br class="">
When N (the number of independent Fouier voxels in
a shell) is large<br class="">
enough, mean(Signal x Noise) ~ 0.0 is only an
approximation, but a pretty<br class="">
good one, even for a single FSC experiment. This
is why, in my book,<br class="">
derivations that depend on Frank & Al-Ali are
OK, under the strict<br class="">
assumption that N is large. Numerically, this
becomes apparent when Marin's<br class="">
half-bit criterion is plotted - asymptotically it
has the same behavior as<br class="">
a constant threshold.<br class="">
<br class="">
So, is Marin wrong to worry about this? No, I
don't think so. There are<br class="">
indeed cases where the assumption of large N is
broken. And under those<br class="">
circumstances, any fixed threshold (0.143, 0.5,
whatever) is dangerous.<br class="">
This is illustrated in figures of van Heel &
Schatz (2005). Small boxes,<br class="">
high-symmetry, small objects in large boxes, and a
number of other<br class="">
conditions can make fixed thresholds dangerous.<br
class="">
<br class="">
It would indeed be better to use a non-fixed
threshold. So why am I not<br class="">
using the 1/2-bit criterion in my own work? While
numerically it behaves<br class="">
well at most resolution ranges, I was not
convinced by Marin's derivation<br class="">
in 2005. Philosophically though, I think he's
right - we should aim for FSC<br class="">
thresholds that are more robust to the kinds of
edge cases mentioned above.<br class="">
It would be the right thing to do.<br class="">
<br class="">
Hope this helps,<br class="">
Alexis<br class="">
<br class="">
<br class="">
------------------------------<br class="">
<br class="">
Message: 2<br class="">
Date: Fri, 21 Feb 2020 17:19:00 +0000<br class="">
From: "Ludtke, Steven J." <<a
href="mailto:sludtke@bcm.edu" target="_blank"
class="" moz-do-not-send="true">sludtke@bcm.edu</a>><br
class="">
To: Alexis Rohou <<a
href="mailto:a.rohou@gmail.com" target="_blank"
class="" moz-do-not-send="true">a.rohou@gmail.com</a>><br
class="">
Cc: "Pawel A. Penczek" <<a
href="mailto:Pawel.A.Penczek@uth.tmc.edu"
target="_blank" class="" moz-do-not-send="true">Pawel.A.Penczek@uth.tmc.edu</a>>,
Marin van Heel<br class="">
<<a
href="mailto:marin.vanheel@googlemail.com"
target="_blank" class="" moz-do-not-send="true">marin.vanheel@googlemail.com</a>>,
"<a href="mailto:CCPEM@JISCMAIL.AC.UK" target="_blank"
class="" moz-do-not-send="true">CCPEM@JISCMAIL.AC.UK</a>"<br
class="">
<<a href="mailto:ccpem@jiscmail.ac.uk"
target="_blank" class="" moz-do-not-send="true">ccpem@jiscmail.ac.uk</a>>,
"<a href="mailto:3dem@ncmir.ucsd.edu" target="_blank"
class="" moz-do-not-send="true">3dem@ncmir.ucsd.edu</a>"
<<a href="mailto:3dem@ncmir.ucsd.edu"
target="_blank" class="" moz-do-not-send="true">3dem@ncmir.ucsd.edu</a>>,<br
class="">
"<a href="mailto:CCP4BB@JISCMAIL.AC.UK"
target="_blank" class="" moz-do-not-send="true">CCP4BB@JISCMAIL.AC.UK</a>"
<<a href="mailto:CCP4BB@jiscmail.ac.uk"
target="_blank" class="" moz-do-not-send="true">CCP4BB@jiscmail.ac.uk</a>><br
class="">
Subject: Re: [3dem] Which resolution?<br class="">
Message-ID: <<a
href="mailto:84516CBB-AE8E-49B4-A123-7C6724E93CE2@bcm.edu"
target="_blank" class="" moz-do-not-send="true">84516CBB-AE8E-49B4-A123-7C6724E93CE2@bcm.edu</a>><br
class="">
Content-Type: text/plain; charset="utf-8"<br
class="">
<br class="">
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.<br class="">
<br 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.<br class="">
<br 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 ?, as it would be silly to say
2.3397 +- 0.2.<br class="">
<br 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).<br class="">
<br 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.<br class="">
<br class="">
<br class="">
<br class="">
--------------------------------------------------------------------------------------<br
class="">
Steven Ludtke, Ph.D. <<a
href="mailto:sludtke@bcm.edu" target="_blank"
class="" moz-do-not-send="true">sludtke@bcm.edu</a><mailto:<a
href="mailto:sludtke@bcm.edu" target="_blank"
class="" moz-do-not-send="true">sludtke@bcm.edu</a>>>
Baylor College of Medicine<br
class="">
Charles C. Bell Jr., Professor of Structural
Biology<br class="">
<br class="">
<br class="">
<br class="">
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<div dir="ltr" class="">
<div class="">Prof. Jose-Maria Carazo<br class="">
Biocomputing Unit, Head, CNB-CSIC<br class="">
Spanish National Center for Biotechnology</div>
<div class="">Darwin 3, Universidad Autonoma de Madrid</div>
<div class="">28049 Madrid, Spain</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size:
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<br class="">
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Cell: +34639197980<br class="">
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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="">3dem mailing list</span><br
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;" class="">
<a href="mailto:3dem@ncmir.ucsd.edu" style="font-family:
Helvetica; font-size: 18px; font-style: normal;
font-variant-caps: normal; font-weight: normal;
letter-spacing: normal; orphans: auto; text-align:
start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-size-adjust: auto;
-webkit-text-stroke-width: 0px;" class=""
moz-do-not-send="true">3dem@ncmir.ucsd.edu</a><br
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;" class="">
<a
href="https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_mailman_listinfo_3dem&d=DwICAg&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=xmaCSRNPE3u67PDAef4f-xpFdDA-9JanE7OO-BicWjE&s=3OTi19FGwT17NSo9ukTyFi9XYR3xR4L54AR2cjs2ilI&e="
style="font-family: Helvetica; font-size: 18px;
font-style: normal; font-variant-caps: normal;
font-weight: normal; letter-spacing: normal; orphans:
auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-size-adjust: auto;
-webkit-text-stroke-width: 0px;" class=""
moz-do-not-send="true">https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_mailman_listinfo_3dem&d=DwICAg&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=xmaCSRNPE3u67PDAef4f-xpFdDA-9JanE7OO-BicWjE&s=3OTi19FGwT17NSo9ukTyFi9XYR3xR4L54AR2cjs2ilI&e=</a><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></div>
</blockquote>
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<pre class="moz-quote-pre" wrap="">_______________________________________________
3dem mailing list
<a class="moz-txt-link-abbreviated" href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>
<a class="moz-txt-link-freetext" href="https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem">https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem</a>
</pre>
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