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I have a set of experimental data, say x and y, where both x and y have experimental error following a normal distribution with different sigma. I want to fit the data y=f(x) to get some parameters that describe the physics. The final goal is to apply the regressed parameters in another numerical model to get one single result, say omega.

My question is how to determine the error of omega. I was thinking about using bootstrap to resample the experimental data, do the numerical computation and repeat many times to get the final result. But what to do with my experimental error? Is it also allowed to resample from the experimental error following a normal distribution. Then there will be two nested bootstrap, which makes things a little bit complicated... Does anyone know if there is any link or material that explain this type of problem?

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  • $\begingroup$ You usually apply bootstrap when you have a single statistic and you want to obatain a distribution / confidence intervals from that statistic. If you already have distributed data, bootstrap is not useful. When you say 'describe the physics'; what do you exactly mean? $\endgroup$
    – smndpln
    Commented Nov 28, 2016 at 23:27
  • $\begingroup$ I have an equation relating x and y, there are some unknown parameters in the equation. I want to fit the equation with experimental data points. And then use the fitted parameters in another numerical simulation. In order to get the inference of the numerical simulation result, I was thinking to use bootstrap to propagate the error. Does this make sense? $\endgroup$
    – Xin
    Commented Nov 29, 2016 at 12:59
  • $\begingroup$ I think you should explicitely say what do you want to fit, and on what. What do your data represent? What equation do you mean? $\endgroup$
    – smndpln
    Commented Nov 30, 2016 at 8:42
  • $\begingroup$ Thanks for your comment. I was aware that this description is not very clear. So I put a more detailed question in here. stats.stackexchange.com/questions/248638/… $\endgroup$
    – Xin
    Commented Nov 30, 2016 at 10:12

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Is it a straight-line relationship between the variables?

With errors in y and x, you could try the York method.

D. York, N. Evensen, M. Martinez, J. Delgado "Unified equations for the slope, intercept, and standard errors of the best straight line" Am. J. Phys. 72 (3) March 2004.

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