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I want to estimate the uncertainty of a calculation which involves a quantity from a fitted mathematical model. More specifically, the end calculation would be something like:

P = x / A_tot

where I know the uncertainty of the x quantity. Given the uncertainty of A_tot I could then estimate the uncertainty of P with standard error propagation techniques. The problem is that A_tot is given not by experiments but comes from a fitted model with the following form:

equation 1

where f(r) is a Gaussian distribution:

fr

rp and sp are the fitted parameters, for which I have the confidence intervals, and r the independent variable.

From my model I only get a value of A_tot, which is that obtained with the best guess of my parameters. How can I estimate the uncertainty of the value of Atot so that I could use it in my final error estimation? Or should I consider it as a constant?

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  • $\begingroup$ Because the numerator is always infinite--the integral diverges towards $+\infty$ at the lower limit--it's difficult to proceed except to reply something like "the uncertainty is always infinite" or "this makes no sense at all." $\endgroup$ – whuber Feb 25 '19 at 13:40
  • $\begingroup$ Thanks for the feedback. I have editted the question and hope it's more clear now. $\endgroup$ – egil137 Feb 25 '19 at 15:25
  • $\begingroup$ There must still be something wrong with your statement of the model, because the numerator is always divergent, no matter what the fitted parameters may be. $\endgroup$ – whuber Feb 25 '19 at 15:52
  • $\begingroup$ well the model is widely used in the literature. I take it that this model doesn't allow for an uncertainty calculation of its results then.Thank you. $\endgroup$ – egil137 Feb 26 '19 at 14:00
  • $\begingroup$ I urge you to make a detailed comparison of the formula you have presented and what you find in the literature. I doubt there is any literature on a model that cannot exist mathematically! $\endgroup$ – whuber Feb 26 '19 at 14:07