Curve fitting
Curve fitting hints
This is a very difficult subject and should only be considered
by experienced users who really understand the mathematics of
the model and are fully aware of any singularities and
bifurcations.
If it is at all possible you should refrain from
fitting the inital conditions as parameters, or at least constrain them
to stay within a narrow range, as inaccurate initial conditions introduce
many complications.
Fitting will only be succesful if you have
extensive accurate data, the correct model, and good starting
estimates.
Consider these hints.
- If you only have a single equation you may find that program
QNFIT gives you more control over the fitting and offers
more options for plotting and goodness of fit.
- Create a library file (like deqsol.tfl) to facilitate the
choice of parameter starting estimates and limits.
- Try to fix the initial conditions y0(i), or only vary these
within a narrow range if it is absolutely necessary.
- As the integration always starts at x = 0 and assumes that
the y0(i) refer to y(i) at x = 0, you should try to obtain
some data close to x = 0 if at all possible.
- After choosing starting estimates, integrate and overlay to
make sure a sensible starting position is being employed.
- Do not estimate the covariance matrix unless you are sure
that the parameter standard errors are going to be helpful.
The estimation can be time consuming, and standard
errors are not very accurate and are seldom very useful.
- If you pick random fitting, DEQSOL generates pseudo random
normal, or uniform, numbers between parameter limits, and it
will only overwrite the current parameters if a solution is
found with a smaller objective function.
This technique should
be used sparingly, with narrow parameter limits, and then
only if you suspect that a local minimum is being detected.
- If you use a single fitting you will be able to observe the
progress of optimisation, but if you choose random fitting
then only the final results will be displayed.
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