Mathematica Curve Fitting With Uncertainties

In summary, the conversation is discussing the possibility of fitting a nonlinear model to a set of data points that have uncertainties on both the x and y values. The use of the Weights command is mentioned as a way to incorporate the y uncertainties, but the questioner is unsure of how to also include the x uncertainties. A link is provided for further reading on "errors in variables" and how to handle them in curve fitting.
  • #1
Screwdriver
129
0
I have a set of data points [itex]\{\{x_1, y_1\}, \{x_2, y_2\} ... \}[/itex] each with an uncertainty [itex]\{\{dx_1, dy_1,\}, \{dx_2, dy_2\} ...\}[/itex]. Is there any way of fitting a nonlinear model to the data that incorporates the uncertainties on both [itex]x[/itex] and [itex]y[/itex]? I know that you can use the Weights command to incorporate the uncertainties on the [itex]y[/itex] values, but I don't know how to get the [itex]x[/itex] uncertainties in there as well.
 
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  • #2
Screwdriver said:
I have a set of data points [itex]\{\{x_1, y_1\}, \{x_2, y_2\} ... \}[/itex] each with an uncertainty [itex]\{\{dx_1, dy_1,\}, \{dx_2, dy_2\} ...\}[/itex]. Is there any way of fitting a nonlinear model to the data that incorporates the uncertainties on both [itex]x[/itex] and [itex]y[/itex]? I know that you can use the Weights command to incorporate the uncertainties on the [itex]y[/itex] values, but I don't know how to get the [itex]x[/itex] uncertainties in there as well.

You need to read up on "errors in variables":

http://www.wavemetrics.com/products/igorpro/dataanalysis/curvefitting/errorsinvariables.htm
 

Related to Mathematica Curve Fitting With Uncertainties

1. What is Mathematica Curve Fitting With Uncertainties?

Mathematica Curve Fitting With Uncertainties is a feature in the software program Mathematica that allows users to fit curves to data sets while taking into account uncertainties in the data points. This feature is useful for scientists who need to accurately model and analyze experimental data.

2. How does Mathematica Curve Fitting With Uncertainties work?

Mathematica Curve Fitting With Uncertainties uses a Bayesian approach to curve fitting, which takes into account the uncertainties in the data points and gives a more accurate representation of the data. The software uses algorithms and statistical techniques to find the best fit curve for the data set.

3. Can I use Mathematica Curve Fitting With Uncertainties with any type of data?

Yes, Mathematica Curve Fitting With Uncertainties can be used with any type of data, including numerical, textual, and symbolic data. It can also handle data sets with large numbers of data points.

4. How accurate is Mathematica Curve Fitting With Uncertainties?

The accuracy of Mathematica Curve Fitting With Uncertainties depends on the quality and quantity of the data points. With a large and well-distributed data set, the curve fitting results can be highly accurate. However, it is important to note that uncertainties in the data can still affect the accuracy of the curve fitting.

5. Are there any limitations to using Mathematica Curve Fitting With Uncertainties?

One limitation of Mathematica Curve Fitting With Uncertainties is that it assumes the data points have Gaussian uncertainties. If this assumption is not met, the results may not be as accurate. Additionally, the software may take longer to process and analyze large data sets with a large number of uncertainties.

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