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:
where f(r) is a Gaussian distribution:
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?