Chronological Thread 

< Chronological >      < Thread >

---

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] SBML L3 dist package, Andrew Miller, 05/25/2011

---

Archive powered by MHonArc 2.6.18.