Fit using nlinfit with uncertainties on x and y accounted for in the fit

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Henriette Ravn Larsen 2021-8-24

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编辑： Henriette Ravn Larsen 2021-8-26

I would like to include uncertainties on x values and y values during the fit procedure such that the uncertainties are accounted for during the fitting. I am currently using the matlab function nlinfit as I am dealing with a mono-exponential decay but I am open to using another fit function if this does the job.

Can anyone tell me how to do that?

Thanks, Henriette

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回答（2 个）

Bjorn Gustavsson 2021-8-25

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Have a look at the total least squares tools on the file exchange: total-least-squares-with-mixed-and-or-weighted-disturbances and total-least-squares-method - they might at least give you somewhere to start solving this type of problem (which is much more intricate than the standard least-squares fitting-problem...).

HTH

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Henriette Ravn Larsen 2021-8-25

Thanks, I will take a look at that

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Image Analyst 2021-8-25

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Not sure what you mean. Of course all fitting routines can handle "uncertainties" in x and y in that they don't expect the actual data to lie perfectly on the fitted line. Attached is a demo of how to use fitnlm() to get exponential decay formula:

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Bjorn Gustavsson 2021-8-25

@Image Analyst, there are some additional complexities with uncertainties in both x and y - see for example the wikipedia-page on Total_least_squares. The standard fitting-functions only do the normal least-square-fitting as far as I know.

Henriette Ravn Larsen 2021-8-26

编辑：Henriette Ravn Larsen 2021-8-26

@Image Analyst

I think you still misunderstand me. No, u_x and u_y is not just to add noise, they are the associated uncertainties to the x- and y-values. Those that you would also put on as errorbars. The data is worth nothing without the uncertainties. And since the uncertainty can vary a lot from datapoint to datapoint I would like to take that into account in the fitting - like a weighting, but where I actually give the uncertainties for x- and y-values.

Makes more sense now? :)

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