Hi Darryl,

`I'm working on approaches for representing parameter uncertainty in`

`CellML, and was wondering if you had any more recent draft`

`specifications for the SBML dist package than the 2005 version on the`

`SBML site (which currently only seems to have the 2005 draft and your`

`presentation from 2010) that you were willing to share?`

`I think the realisastions based approach discussed in your 2010`

`presentation could be a good way to go in CellML for representing`

`distributions, alongside either a fixed set of univariate and`

`multivariate distributions or a general facility for describing a`

`distribution (possibly as a series of univariate distributions,`

`optionally conditional on other parameters, including other randomly`

`sampled parameters) from p.d.fs (solver software would either pattern`

`match for known p.d.fs, or try to analytically or numerically invert the`

`function).`

`We obviously also need some kind of operator to say that a parameter has`

`a fixed but uncertain value, and that a given distribution is the`

`probability distribution for the parameter (I think using MathML to`

`describe that, with a csymbol operator, would be the most consistent`

`with the approach taken in CellML); for example, if we believe that`

`parameter x has a fixed value:`

e.g. x(0) ~ N(mu=0, sigma^2 = 1) <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#uncertainWithDistribution"/>`

<apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#atBoundVariableValue"/>`

<ci>x</ci> <cn cellml:units="second">0</cn> </apply> <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#distributionFrompdf"/>`

<apply> <csymbol definitionURL="http://www.cellml.org/1.2#normalpdf"/> <cn cellml:units="metre">0</cn> <cn cellml:units="square_metre">1</cn> </apply> </apply> </apply> Or (x(0), y(0)) ~ a distribution from realisations... <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#uncertainWithDistribution"/>`

<vector> <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#atBoundVariableValue"/>`

<ci>x</ci> <cn cellml:units="second">0</cn> </apply> <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#atBoundVariableValue"/>`

<ci>y</ci> <cn cellml:units="second">0</cn> </apply> </vector> <apply>

`<csymbol`

`definitionURL="http://www.cellml.org/1.2#distributionFromRealisations"/>`

`<!-- For consistency with the univariate case, this represented`

`in MathML as a 'vector of vectors' rather than a matrix; we could`

`perhaps treat a MathML matrix as syntactic sugar for a vector of vectors`

`anyway. -->`

<vector> <vector><cn units="metre">1</cn><cn units="metre">2</cn></vector> <vector><cn units="metre">3</cn><cn units="metre">3</cn></vector> <vector><cn units="metre">1</cn><cn units="metre">5</cn></vector> <vector><cn units="metre">2</cn><cn units="metre">4</cn></vector> <vector><cn units="metre">1</cn><cn units="metre">5</cn></vector> <vector><cn units="metre">1</cn><cn units="metre">3</cn></vector> <vector><cn units="metre">3</cn><cn units="metre">5</cn></vector> <vector><cn units="metre">2</cn><cn units="metre">5</cn></vector> <vector><cn units="metre">1</cn><cn units="metre">4</cn></vector> <vector><cn units="metre">3</cn><cn units="metre">5</cn></vector> <!-- And so on - obviously this could lead to big files... --> </vector> </apply> </apply> Any comments you may have on this approach would be greatly appreciated. Best wishes, Andrew _______________________________________________ cellml-discussion mailing list cellml-discussion@cellml.org http://lists.cellml.org/mailman/listinfo/cellml-discussion