Calculating standard deviation from a confidence interval?

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!

Answer 1

[Daniel Shub]

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.

[John]

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]

This is more of a statistics question than a MATLAB question.

Answer 2

[Andrew Newell]

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.

[Daniel Shub]

If I remember correctly it is in fact norminv(0.975)*sigma=1.9600*sigma.

[Andrew Newell]

Right. I was remembering a rule of thumb.