# Error analysis and propagation

## Main Question or Discussion Point

Hi folks,

I have a rather simple question on error propagation - I have 2 sets of models, where the results from model are used as variables in the next model. I need to know how to carry forward errors from one to another.

Case -

Model 1: Y = a*exp(b*X) + c

The errors on X (which is a vector of about 100 samples) and Y (a vector of same size as X) are not know. From fitting the above non-linear model to the data and examining the residuals, I can calculate Mean Absolute Error, RMSE, etc. So, in the end I get a vector of Y values and a single error estimate from the model (e.g. RMSE).

Model 2: Z = s*(Y)^t + u

Where Y is the variable obtained from the results of Model 1. Applying Model 1 to a large number of new X values, I now have Y as a vector with > 10,000 elements. Each element in vector Y should have an associated error. My question is - what error should I give each element of vector Y? My next question is, once the error on each element of vector Y is known, how do I propagate this error to each element of vector Z? Finally, how do I calculate RMSE for Model 2?

All help will be much appreciated!

Thanks,
Yaal

## Answers and Replies

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Dale
Mentor
If your process involves nonlinearity and complicated methods then your best bet will be to use some bootstrapping technique to get an estimate of the errors in Z.

http://en.wikipedia.org/wiki/Bootstrapping_(statistics [Broken])

Last edited by a moderator:
Dale
Mentor
Thanks