Calculating standard deviation from a confidence interval?

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John
John 2012-1-6
Hello, I'm using the fit function to do some nonlinear regression fitting, and I have a set of data with n data points and I am fitting the data to a model which contains 3 parameters.
I can get a confidence interval from the fit_object created by the fit function for each parameter, but how can I calculate the standard deviation for each parameter using these confidence intervals?
Thank you!

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回答（2 个）

Daniel Shub
Daniel Shub 2012-1-9
I don't think you can. The standard deviation is going to depend on the distribution of the observations much more so than the confidence intervals. For example, consider (sorry for the poor formating)
x = -a (p = 0.025)
0 (p = 0.95)
a (p = 0.025)
and
y = -a (p = 0.025)
-a+e (p = 0.475)
a-e (p = 0.475)
a (p = 0.025)
x and y will have the same mean and 95% confidence intervals, but different standard deviations.
  2 个评论
John
John 2012-1-9
Thank you, is there any alternative way to estimate the error, or uncertainty associated with each parameter then, or is the confidence interval really the best one can do?
Daniel Shub
Daniel Shub 2012-1-10
This is more of a statistics question than a MATLAB question.

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Andrew Newell
Andrew Newell 2012-1-9
If the underlying distribution of the coefficients is normal, the 95% confidence interval is [mean-2*sigma,mean+2*sigma], so the standard deviation is 1/4 the width of the interval. I'm not sure if that applies to nonlinear regression fitting.

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