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distrib - Uncertainty, distributions, and random numbers package for SBML L3

This proposed package was discussed at the Seattle Hackathon:

http://sbml.org/Events/Hackathons/The_2010_SBML-BioModels.net_Hackathon

I presented an overview of the problem:

Slides: http://sbml.org/images/3/3b/Djw-sbml-hackathon-2010-05-04.pdf
Audio: http://sbml.org/images/6/67/Wilkinson-distributions-2010-05-04.mov

building on the old proposal from the Newcastle group:

http://sbml.org/Community/Wiki/SBML_Level_3_Proposals/Distributions_and_Ranges

There was broad support at the meeting for development of such a
package, and for the proposed feature set. Discussion following the
presentation led to a consensus on the following points:

* There is an urgent need for such a package

* It is important to make a distinction between a description of
* uncertainty regarding a model parameter and the mechanistic process
* of selecting a random number from a probability distribution, for
* applications such as parameter scans and experimental design

* It is probably worth including the definition of PMFs, PDFs and CDFs
* in the package

* It is worth including the definition of random distributions using
* particle representations within such a package, though some work
* still needs to be done on the precise representation

* It could be worth exploring the use of xinclude to point at particle
* representations held in a separate file

* Random numbers must not be used in rate laws or anywhere else that
* is continuously evaluated, as then simulation behaviour is not
* defined

* Although there is a need for a package for describing extrinsic
* noise via stochastic differential equations in SBML, such mechanisms
* should not be included in this package due to the considerable
* implications for simulator developers

* We probably don't want to layer on top of UncertML
* (www.uncertml.org), as this spec is fairly heavy-weight, and
* somewhat tangential to our requirements

* A random number seed is not part of a model and should not be
* included in the package

* The definition of truncated distributions and the specification of
* hard upper and lower bounds on random quantities should be
* considered.

It was suggested that new constructs should be introduced into SBML by
the package embedded as user-defined functions using the following
syntax:

<listOfFunctionDefinitions>
<functionDefinition id="myNormRand">
<distrib:####>
#### distrib binding information here ####
</distrib:####>
<math>
<lambda>
<bvar>
<ci>mu</ci>
<ci>sigma</ci>
</bvar>
<ci>mu</ci>
</lambda>
</math>
</functionDefinition>
</listOfFunctionDefinitions>

which allows the use of a "default value" by simulators which do not
understand the package (but simulators which do will ignore the <math>
element). The package would nevertheless be "required", as it will not
be simulated correctly by software which does not understand the
package.

Informal discussions following the break-out covered topics such as
how to work with vector random quantities in the absence of the vector
element in the MathML subset used by SBML, and the care that must be
taken with the semantics of random variables and the need to both a)
reference multiple independent random quantities at a given time and
b) make multiple references to the same random quantity at a given
time.


Constructive comments on any of this are welcome.

Regards,

Darren

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