# Finding optimal values from the results of parameter estimation repeats

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### Deepa

Sep 12, 2022, 10:01:07 AM9/12/22
to COPASI User Forum
Hello Everyone,

I performed a parameter estimation repeat (i.e. 1000 parallel runs with the same
initial values of parameters); the estimation task was run via Cloud Copasi. I
am trying to estimate ~20 parameters using steady-state measurements from
experiments.

After running the estimation task (using Evolution strategy algorithm) for 10 hours (using --maxTime argument), the results were obtained.

When I look at the distribution of the objective values, the values fall in the range  (900, 2000).  There are several combinations of parameter values that I obtain for objective values that lie in the same order of magnitude. I understand increasing the duration of the estimation run may decrease the objective value further, but I think I would still end up with several sets of parameter values.

I would like to ask for suggestions on how to process these results.
If there are some references that I could read to understand how to cluster these results and find an optimal parameter set, that would be of great help.

Thank you very much for your time and kind attention,
Deepa

### Sluka, James Patrick

Sep 12, 2022, 4:29:03 PM9/12/22

As a starting point just look for correlations among the parameters. Often you get strong correlations for things like the Vmax and Km in a Michaelis-Menten relationship. If the system never saturates then it is really first order with rate constant k=Vmax/Km, but Vmax and Km can vary widely, as long as the ratio is constant. So you will get multiple sets of Vmax, Km but the ratio is constant. (That tells you to just replace the MM with first order).

Also, for a sequence of reactions that are undetermined you will sometimes get a rate limiting step moving up and down the chain of reactions. For example, A->B->C, if little is known about B then often a fast first and slow second step is the same as reversing the speeds. This too will often show up as correlations.

Another thing to consider is the sensitivity of the output to your parameters at the solution sets. Does the output change if you change the individual parameters? This can be tricky to measure since if you really have optimized a parameter then the sensitivity at the optimal value of the parameter may well be zero. So, you’ll want to take big sensitivity steps, perhaps as much as 50%. (Compared to the often suggested steps of less than 1%)

I hope that helps a bit.

Jim

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