Bart

Yes, I think Peter's original question arose in the context of
predicting Rfree.  For that we have to consider the *total* restraint
count separately from the total observation count, and provided each
restraint is independent of all other restraints it counts as one, and
similarly provided the observations are statistically independent they
each count as one (of course they have to be 'real' observations: an
Fobs with a very large uncertainty would effectively have zero weight
and would not be counted since it tells you nothing about the parameters
- notice that it's the magnitude of the standard uncertainty that
matters *not* the ratio Fobs/SU as some people would have you believe!).

Of course the restraints are not independent of the observations in the
sense that most parameters will be affected by both the restraints and
the observations and as you say the refined parameters must depend on
the relative overall weights.  So one has to adjust the total restraint
count relative to the total observation count to compensate for this.
There is a correction factor in the equation for <Rfree/Rwork> which
takes care of this.

-- Ian 

> -----Original Message-----
> From: Bart Hazes [mailto:[log in to unmask]] 
> Sent: 14 February 2008 18:32
> To: Ian Tickle
> Cc: [log in to unmask]
> Subject: Re: [ccp4bb] counting constraints?
> 
> 
> Thanks Ian,
> 
> I saw experimental observations and restraints (empirical 
> observations) 
> as completely different but I now see they are just two different 
> sources of information that restrain the model parameters. So 
> when you 
> are counting they can all get "one vote" as long as the 
> observations are 
> independent. However, from an information content point of view the 
> weight, or the standard deviation for Fobs, should still matter when 
> multiple observations/restrains affect a model parameter.
> 
> For instance, torsion angle restraints tend to have broad 
> distibutions 
> leading to low weights and I would expect adding them as 
> observations to 
> the refinement will not contribute greatly to the "available 
> information" to define the model, unless there is not much 
> information 
> from other sources to start with. In the recent posting of using 
> secondary structure conformational restraints at 3.6A this 
> may start to 
> make a difference.
> 
> Bart
> 
> Ian Tickle wrote:
> > Peter, Bart
> > 
> > Actually the restraint weight doesn't affect the restraint count one
> > iota and as far as counting is concerned each restraint has 
> exactly one
> > 'vote' in the count.  However there is an important proviso: the
> > restraints must be completely independent to contribute fully to the
> > count.  Suppose you have a torsion restraint say on an methoxyphenyl
> > group (an example close to my heart since we have endless 
> debates about
> > it!), and suppose the weight on the restraint is absolutely 
> miniscule,
> > but still non-zero (we'd better say it's > than the machine 
> precision to
> > avoid rounding problems).  Provided no other restraint or 
> observation
> > (restraints and observations are of course essentially the 
> same thing)
> > affects that torsion angle it will have its full effect, in fact the
> > effect won't depend on the weight.  Of course as soon as 
> you have other
> > restraints which affect that same torsion angle they will 
> compete with
> > each other depending on their relative weights, and you 
> can't count them
> > as independent any more.
> > 
> > To answer Peter's original question each *active* restraint 
> is counted.
> > The question of inactive restraints becomes relevant when 
> considering
> > e.g. VDW restraints which normally only become active when 
> the distance
> > becomes less than a threshold.
> > 
> > -- Ian
> > 
> > 
> >>-----Original Message-----
> >>From: [log in to unmask] 
> >>[mailto:[log in to unmask]] On Behalf Of Bart Hazes
> >>Sent: 14 February 2008 15:53
> >>To: Meyer, Peter
> >>Cc: [log in to unmask]
> >>Subject: Re: [ccp4bb] counting constraints?
> >>
> >>Hi Pete,
> >>
> >>In your example it would count as 4 restraints, not 
> constraints, and 
> >>certainly not 4 observations or 4 parameters. It is not clear 
> >>to me how 
> >>to quantify the information content in restraints, it 
> >>probably depends 
> >>on the type of restraint and surely on the weight. Maybe 
> information 
> >>theory has some ideas if you are really interested.
> >>For real constraints, which fix parameters of the model one way or 
> >>another, it may be easier. For instance imposing exact NCS 2-fold 
> >>symmetry reduces the parameters by a factor of 2.
> >>
> >>Bart
> >>
> >>Meyer, Peter wrote:
> >>
> >>>Hi,
> >>>
> >>>The recent discussion on Rwork/Rfree ratio reminded me of 
> >>
> >>something I was wondering about (*).  When counting 
> >>constraints as observations for determining the observation 
> >>to parameter ratio, is each unique constraint counted, or 
> >>each time a given constraint is used.  For example, if there 
> >>are 4 carbon oxygen bonds (assuming the same parameters, 
> >>let's say serine beta-carbon to serine gamma-oxygen), would 
> >>this count as 4 constraints as observations, or 1?
> >>
> >>>Intuitively, it seems to me like it should be counting 
> >>
> >>unique constraints (although as near as I can tell these 
> >>aren't listed in refmac5 logfiles).  But I don't have a clear 
> >>explanation for why, and of course I could be wrong on this.  
> >>
> >>>
> >>>Thanks,
> >>>
> >>>
> >>>Pete
> >>>
> >>>* Rough translation - I'm about to ask another stupid 
> >>
> >>question.  Not like it's the first time.
> >>
> >>>
> >>
> >>-- 
> >>
> >>==============================================================
> >>================
> >>
> >>Bart Hazes (Assistant Professor)
> >>Dept. of Medical Microbiology & Immunology
> >>University of Alberta
> >>1-15 Medical Sciences Building
> >>Edmonton, Alberta
> >>Canada, T6G 2H7
> >>phone:  1-780-492-0042
> >>fax:    1-780-492-7521
> >>
> >>==============================================================
> >>================
> >>
> >>
> > 
> > 
> > 
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> 
> -- 
> 
> ==============================================================
> ================
> 
> Bart Hazes (Assistant Professor)
> Dept. of Medical Microbiology & Immunology
> University of Alberta
> 1-15 Medical Sciences Building
> Edmonton, Alberta
> Canada, T6G 2H7
> phone:  1-780-492-0042
> fax:    1-780-492-7521
> 
> ==============================================================
> ================
> 
> 


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