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Topic: Fitting multiple data sets to multiple functions with shared fit parameters
Replies: 1   Last Post: Jan 7, 2013 11:05 PM

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 Daniel Lichtblau Posts: 1,761 Registered: 12/7/04
Re: Fitting multiple data sets to multiple functions with shared fit parameters
Posted: Jan 7, 2013 11:05 PM

On Sunday, January 6, 2013 11:35:58 PM UTC-6, dr DanW wrote:
> I am a an experienced user of Mathematica and am used to fitting complex valued functions to data sets, but only one function at a time. I am attempting to determine the parameters in a model of a physical system (an acoustic transducer). From the model, I can determine several transfer functions over frequency or the Laplace s, and I can also measure these transfer functions on a device. This gives me, for example, three functions (which share parameters) and three data sets, and I want to find the parameters that fit all three functions to their respective data sets simultaneously. The parameters in the model are real, but the functions and data are complex. Another complication is that the data sets have different units and scales, so I will need to normalize things so \chi^2 on all curves are weighted equally.
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> Is there a way to directly use the built in FindFit or NonlinearModelFit to solve this problem? If not, can anyone suggest how I could construct my own method using NMinimize? I would be very grateful if the group could point me toward an example where this as been done.
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> Regards,
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> Daniel

The following links may help. I'm sure there are others as well; this has come up a number of times in comp.soft-sys.math.mathematica.

http://forums.wolfram.com/mathgroup/archive/2010/Apr/msg00280.html
http://forums.wolfram.com/mathgroup/archive/2012/May/msg00289.html

Daniel Lichtblau
Wolfram Research

Date Subject Author
1/7/13 Daniel Warren
1/7/13 Daniel Lichtblau