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Re: Fitting multiple datasets to "partially" the same model (global fit

From: Olaf Till
Subject: Re: Fitting multiple datasets to "partially" the same model (global fit with shared parameters)
Date: Mon, 7 Dec 2015 16:15:59 +0100
User-agent: Mutt/1.5.23 (2014-03-12)

On Mon, Dec 07, 2015 at 06:32:56AM -0800, JokerOne wrote:
> Hello everybody,
> I am looking for an Octave solution for a task I manage to perform in
> Origin, i.e. it appears possible from the mathematical point of view.
> However, I have no idea, how to solve it in Octave, which I desire:
> I like to fit a model curve to a number of datasets, say
> data1 = [x,y1]
> data2 = [x y2]
> ...
> the number of datasets is in the order of 10 (i.e. not many more).
> The model to that data is something like:
> F(x) = f(x) * g(x), where
> f(x) depens on some fitting parameters, say a0, a1, a2,...
> and g(x) depends on b0, b1,...
> Now I would like to fit all data with the same model simultaneously making
> use of my knowledge, that the parameters of g(x) (i.e. b0, b1,...) are equal
> for all the datasets.
> For example, my model function is:
> F(x) =  ( a0*ln(x) )* (b0+b1*x) 
> with b0, b1 equal for all datasets.

What do you mean by saying some parameters are "equal for all
datasets"? If a parameter is different for a different dataset, it is
a different parameter, not the same one.

In which way do you want to make use of your knowledge, that ... are
"equal for all the datasets"?

Do you want

on the one hand: a common name for accessing a set of parameters, each
applying to a different dataset,

and on the other hand: a name for accessing a parameter applying to
all datasets?

Then there is something in the 'optim' package you could use.

Or do you mean that certain parameters affect all datasets, and
certain parameters affect only one dataset each? But this is not how
you explained it.

Or what else?


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