This also depends on how you have set up the statistical problem, and
what statistical philosophy you adhere to. If you have a hierarchical
model (which can fit in a likelihood paradigm) or you are a Bayesian,
then all of these values are random variables.
This argument is mostly just semantics, but I tend to agree with
Gerard. In statistics the RMS deviation is the standard deviation,
and that measure is not what RMSD refers to in structural biology. I
prefer to use the variance or standard dev, personally. The two are
related by the simple equation:
RMSD^2 = 2 * Var
if you use the unbiased sample variance (N-1 in denom), otherwise
RMSD^2 = 2N * Var / (N-1)
which can be calculated per atom, or if you assume every atom has the
same deviation/variance, for the entire structure.
On Apr 9, 2008, at 9:32 AM, Ed Pozharski wrote:
> You originally referred to statistics, and from statistical point of
> view different structures have different underlying probability
> distributions. In statistics the rms DEVIATION (or standard
> deviation)
> refers to the variation of a random variable. With rms DISTANCE
> between
> two structures you are not looking at a random variable, you are
> looking
> at the ensemble of random variables (each being the distance between
> two
> homologous atoms). So from STATISTICAL point of view, it is not an
> example of rms deviation. These are semantics, of course, but I hope
> this is the clarification you asked for.
>
> You're welcome anyway...
>
> Ed.
>
> 1. On Tue, 2008-04-08 at 21:33 +0200, Philippe DUMAS wrote:
>> Apparently I had missed some subtle considerations...
>>
>> Yet, I confess am not fully convinced: is it so wrong to speak of
>> how much
>> different structures DEVIATE from each other ? I do not see what
>> prevents
>> you from defining the correct underlying probability distribution.
>> That
>> interatomic distances can be used to quantify deviations does not
>> hurt me so
>> much.
>>
>> Thank you anyway...
>>
>> Philippe Dumas
>> IBMC-CNRS, UPR9002
>> 15, rue René Descartes 67084 Strasbourg cedex
>> tel: +33 (0)3 88 41 70 02
>> [log in to unmask]
>>
>>
>>
>>
>>
>> -----Message d'origine-----
>> De : Ed Pozharski [mailto:[log in to unmask]]
>> Envoyé : Tuesday, April 08, 2008 3:56 PM
>> À : Philippe DUMAS
>> Cc : [log in to unmask]
>> Objet : Re: [ccp4bb] Help with Superpose results
>>
>>
>> RMS deviation refers to the variance of a random variable - it is a
>> characteristic of the underlying probability distribution. When you
>> superpose two different structures, you are looking at the DISTANCE
>> between atoms, not the DEVIATION in their position. In fact, for
>> individual atoms you can't even say root-mean-square, it's just plain
>> distance. The core argument is that you are looking at two
>> structures
>> that represent different underlying probability distributions, and so
>> it's definitely not the rms deviation you are calculating, but rms
>> distance (rms over all the atoms in the structure). HTH,
>>
>> Ed.
>>
>> On Tue, 2008-04-08 at 11:07 +0200, Philippe DUMAS wrote:
>>> Although this is not a very important issue..., I am a bit
>>> surprised by
>>> Gerard's insistance for a 'stop calling rmsd "rms deviation"'.
>>> Isn'it a
>>> general term in statistical studies, valid for distances separating
>>> homologous atoms as well as for any other factor (B factors for
>>> example) ?
>>>
>>> Philippe Dumas
>>> IBMC-CNRS, UPR9002
>>> 15, rue Rene Descartes 67084 Strasbourg cedex
>>> tel: +33 (0)3 88 41 70 02
>>> [log in to unmask]
>>>
>>>
>>>
>>>
>>> -----Message d'origine-----
>>> De : CCP4 bulletin board [mailto:[log in to unmask]]De la part de
>>> Gerard DVD Kleywegt
>>> Envoye : Monday, April 07, 2008 7:20 PM
>>> A : [log in to unmask]
>>> Objet : Re: [ccp4bb] Help with Superpose results
>>>
>>>
>>>> Is the rms xyz displacement equivalent to an rmsd??
>>>
>>> yes. it is in fact a better name than "rms deviation", although i
>>> think
>>> 'root-mean-square distance' is even better, as it says exactly
>>> what you
>>> calculate.
>>>
>>> think of it like this, the formula for rmsd is:
>>>
>>> RMSD = square-root [ SUM(atoms) { (x1-x2)^2 + (y1-y2)^2 + (z1-
>>> z2)^2 } /
>>> Natoms
>>> ]
>>>
>>> now, "(x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2" is the Square of the
>>> Distance
>>> between
>>> two equivalenced atoms in structure 1 and 2; adding them for all
>>> pairs of
>>> equivalenced atoms and dividing by the number of atoms gives you
>>> the Mean
>>> Squared Distance; finally, taking the square root yields the
>>> Root-Mean-Square
>>> Distance, or RMSD
>>>
>>> so, people, can we all please stop calling rmsd "rms deviation" - it
>> really
>>> is
>>> an "rms distance" (or "rms displacement"). you could argue that the
>> formula
>>> gives some kind of rms coordinate deviation, but in that case you
>>> ought to
>>> divide by 3*Natoms instead.
>>>
>>> (having said that, the term "RMS B displacement" sounds positively
>>> silly!)
>>>
>>> --dvd
>>>
>>> ******************************************************************
>>> Gerard J. Kleywegt
>>> [Research Fellow of the Royal Swedish Academy of Sciences]
>>> Dept. of Cell & Molecular Biology University of Uppsala
>>> Biomedical Centre Box 596
>>> SE-751 24 Uppsala SWEDEN
>>>
>>> http://xray.bmc.uu.se/gerard/ mailto:[log in to unmask]
>>> ******************************************************************
>>> The opinions in this message are fictional. Any similarity
>>> to actual opinions, living or dead, is purely coincidental.
>>> ******************************************************************
>> --
>> Edwin Pozharski, PhD, Assistant Professor
>> University of Maryland, Baltimore
>> ----------------------------------------------
>> When the Way is forgotten duty and justice appear;
>> Then knowledge and wisdom are born along with hypocrisy.
>> When harmonious relationships dissolve then respect and devotion
>> arise;
>> When a nation falls to chaos then loyalty and patriotism are born.
>> ------------------------------ / Lao Tse /
>>
>>
>>
> --
> Edwin Pozharski, PhD, Assistant Professor
> University of Maryland, Baltimore
> ----------------------------------------------
> When the Way is forgotten duty and justice appear;
> Then knowledge and wisdom are born along with hypocrisy.
> When harmonious relationships dissolve then respect and devotion
> arise;
> When a nation falls to chaos then loyalty and patriotism are born.
> ------------------------------ / Lao Tse /
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