I Measurement for uncertainty in nonlinear model

[liquidFuzz]

I would like to find a measurement for uncertainty in a calculation I have. So, the uncertainties I have, or at least as far as I understand.

1. uncertainty of sampled data that is used to optimized parameters of the model.
2. uncertainty in the curve fit procedure

Is there some fairly accessible (I mean cognitive) information about how I should approach this? I remember doing this kind of calculations back when I was studying, but it was a loooong time ago. If anyone could point me in the right direction..?

Thanks in advance!

 

[BvU]

Hi,

Are you referring to propagation of uncertainty ?
Regression error handling ?
If not, can you give an overview of what you have so far ?

[edit]Ah, found this and that , having to do with growth models. Connected ? If so, I'd love to see the data ...

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[liquidFuzz]

Hm. i might have been vague in my post, sry... We could use the growth model example, but I fear it might be to complicated, for me... I have four detector signals Sxx where my output = (Saa - Sab)(Sba - Sbb). The detector is the same so all signals have the same uncertainty. If understand this I should be able to use the Example formulae table, line 3 and 7, in the first link you to get an expression for the variation/standard deviation of my out signal.

 

[liquidFuzz]

I think i understand the subject well enough to implement it in code (which I usually do when I thinker). One question though. To calculate the variance of the function value I take the Jacobian J of the function and the Covariance matrix C of the curve fit and multiply as such v = J C J ^T. Which I then use to calculate my confidence intervals, ci = Z sqrt(v). Is this correct..? And if someone would take a stab at explaining the vector matrix multiplication...

 

[BvU]

Hm. i might have been vague in my post, sry...

Treading carefully is wise...

We could use the growth model example, but I fear it might be to complicated, for me...

If not the growth model, then what model are you using (*) ?
(The guys here use

Marquardt, D.W. 1963. An algorithm for least squares estimation of nonlinear parameters. Journal of the Society of Industrial Applied Mathematics 2:431–441.​

to determine coefficients in a model, but their data (in table 2) are only in the second part of the curve; very unsatisfactory... )

I have four detector signals Sxx where my output = (Saa - Sab)(Sba - Sbb). The detector is the same so all signals have the same uncertainty. If understand this I should be able to use the Example formulae table, line 3 and 7, in the first link you to get an expression for the variation/standard deviation of my out signal.

What are $S_{aa}$ etc ? Voltmeter readings, Scintillator counts, ... ? Are you sure their uncertainties are completely uncorrelated ?

Line 3 being $f = A - B \Rightarrow \sigma_f^2 = \sigma_A^2 + \sigma_B^2 + \sigma_{AB}^2$ ?
Line 7 being $f = \frac A B$ makes me wonder if you mean output = (Saa - Sab)/(Sba - Sbb) instead of (Saa - Sab)(Sba - Sbb) ?

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(*) is 'output' a simple number or a formula with several coefficients you try to find ?

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