Re: Fitting multiple datasets to "partially" the same model (global fit with shared parameters)

[Oliver Heimlich]

On 08.12.2015 12:51, JokerOne wrote:
> Thanks everybody for your effort,
> 
> since I am not too common to the maths in these regression/optimization
> routines it will take be a while to understand your advises.
> 
> Allen asks for some actual data. However, there is no "real" data, yet. For
> my tests I just simulated some data in a simple way .
> 
> Here, I replaced the logaritmic term with a power term to underline that the
> logaritmic term in indeed just an example function as Allen assumed
> correctly. I do not know the function that will suit my final task, yet. I
> am just checking the basic concept of the fitting routine with some example
> functions.
> 

…

>      #    HERE: FOR SIMULATTION PURPOSE USE :
>      #    f(x)      =    b1^(-1*b2*x) * (a0+a1*x+a2*x^2)

…

> #    To solve:
> #    Find parameters a0, a1, a2 and all parameters of b2_list using
> #    a regression/fit routine that makes uses of fact, that a0,a1,a2 are 
> #    equal for all colums in y
> 
> I am very happy for any further advises and help.


Hi Maximilian,

I have used your code and done the fitting with the latest release of
the interval package.  See
http://cursosing.net/octavers/gnuoctave/listing/580-interval-shared-parameter-estimation

Estimated parameters:

a0 ⊂ [1, 1.0648]
a1 ⊂ [-3.0688, -3]
a2 ⊂ [0.5, 0.51124]
b1 ⊂ [1.5, 1.5042]
b2_list =
{
  [1,1] ⊂ [1, 1.008]
  [1,2] ⊂ [1.1935, 1.2064]
  [1,3] ⊂ [1.3935, 1.4064]
  [1,4] ⊂ [1.5928, 1.6063]
  [1,5] ⊂ [1.7926, 1.8062]
  [1,6] ⊂ [1.9902, 2]
}

Apparently the estimation works quite well (as long as you don't add to
much uncertainty to the observed values of y).

Best regards
Oliver