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I agree that these things are subtle, and so my preference would be for these terms to go in the distrib package, where they will be part of a more coherent attempt to describe uncertainty, which is exactly what these terms are attempting to do. In my experience many experimentalists, and some modellers, are rather hazy about (say) the distinction between standard deviation and standard error. The suggested additional term is for standard deviation, but in some cases the standard error will be actually the relevant measure of uncertainty, and it is not possible to convert between these without knowing the sample size. It is very likely that the standard deviation term will be abused due to this confusion. And as Andrew points out, it is not really possible to do much useful with these statistics without some additional assumptions, anyway. One advantage of including such terms in the distrib package is that other mechanisms for describing uncertainty
will be available, which will often be more appropriate, and will almost always be more useful. Another advantage is that support for the distrib package will hopefully be implemented by people who understand these subtleties, and who will therefore be able to provide appropriate tool support to help their statistically-challenged users. 
 
Cheers,

Darren
--
Darren Wilkinson
email: darrenjwilkinson@btinternet.com
www: http://www.staff.ncl.ac.uk/d.j.wilkinson/


________________________________
From: Andrew Miller <ak.miller@auckland.ac.nz>
To: sbml-discuss@caltech.edu
Sent: Monday, 16 July 2012, 20:37
Subject: Re: [sbml-discuss] upper, lower, mean, stdev

On 17/07/12 07:02, Chris J. Myers wrote:
> I think I we should release a distrib package without mutilvariate distributions first.  There should be no problem upgrading the package later.  From Sarah's message, I think we are gravitating towards adding a small, simple package for the mean, stddev, lower, and upper bounds.  This is fine by me.  I think packages can move much faster than core changes.  Keep in mind there are a lot of items being discussed for L3V2, and they will require more discussion.  No need to delay these items for that discussion.

Hi,

I think there is a semantic problem - what does the 'mean', 'stddev',
'lower', and 'upper' actually mean in a modelling sense? Can they be
used for theoretical properties computed from another model (or in the
case of lower and upper, to impose physical limitations)? Unbiased
estimates from experimental data, based on an assumption of a particular
distribution? Statistics computed over particular experimental data
using a formula which might not produce an unbiased estimate?

Doing any kind of inference using statistics someone else has computed
without knowing where they come from is likely to result in wrong and
misleading results, and so for whatever standard is produced to be
meaningful, it needs to either provide a mechanism to allow the modeller
to say exactly what they have done to produce the statistics and what
assumptions they made, or it needs to lay out the semantic meaning of
the attributes in the specification.

I think if we add a small package for such statistics, perhaps it could
be like distrib, except that the (univariate) normal distribution is
assumed and doesn't need to be stated (and there is no other option for
distribution in that package). The interpretation would then be that the
modeller's posterior distribution (i.e. the distribution representing
the modeller's belief about the true value of the parameter, after
taking into account all available evidence) is normal, with this mu
parameter and this sigma parameter.

However, normal posterior distributions are probably quite rare for the
case where modellers start with a prior and update their distribution;
if they start with a normal prior and update it based on data, they will
end up with a normal-gamma distribution, which has four parameters - one
of which equals the mean of the distribution, and four which are not
equal to any of the proposed values for the stats package.

Best wishes,
Andrew

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