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Re: estimating parameters for diffeq model

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16448] Re: [mg16390] estimating parameters for diffeq model
  • From: David Withoff <withoff>
  • Date: Sat, 13 Mar 1999 02:21:53 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

> Imagine the simple growth model x't = a x[t]  (1 - c x[t]). Say I have
> ten experimental values at time t=0 and t = 10. How can I estimate the
> value of "a" and "c" using FindMinimum or some other means. I have
> looked at the FAQ, "How can I fit data to a model that is defined using
> NDSolve"
> (http://www.wolfram.com/support/Math/Statistics/NDSolveFit.html) but
> this doesn't seem to apply, since it describes the case where data is
> collected at various time points for a single replicate rather than at
> identical time points for many replicates. BTW, I have to use NDSolve
> for my model.
> 
> Thanks in advance,
> Manuel Morales

The method described in that web page applies to any fitting problem.
It doesn't matter how many time points there are.  The method is
to construct an expression for a measure of the difference between
the data and the model as a function of the parameters, and then adjust
the parameters to minimize that expression.  That method is
completely general.

The example that you mentioned, however, doesn't appear to be fully
specified.  This is a three-parameter model (a, c, and an initial
value for x[t]).  With data for only two values of t, the minimum
cannot give unique values for three parameters.  Perhaps the actual
problem that you want to solve is well-specified.

Dave Withoff
Wolfram Research


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