I am using NonlinearRegress to fit a numerical model (defined as an interpolation function) to data, since the model itself is an integral with no analytic solution. NonlinearRegress happily finds best-fit parameters, but gives the message:
NonlinearRegress::nodm: NonlinearRegress was unable to compute a design matrix, because it could not find derivatives of the model. Some requested diagnostics may not be able to be generated.
I suppose this is for the obvious reason that it cannot find an analytic derivative of a numerical model?
So, is there any way to make NonlinearRegress evaluate the relevant derivatives numerically, or some other way of getting confidence intervals for the parameters in the fit?
I have attached an example notebook exhibiting this problem, not using my actual data and function (which are quite complicated) but one that can be done both analytically and numerically.
Thanks very much for any suggestions.
Attachment: NonlinearCIs.nb, URL: ,