How to find uncertainties of estimated parameters in Levenberg- Marquardt algorithm

Hello I have used Levenberg-Marquardt algorithm in 3 parameter problem but I unable to estimate uncertainties associated with it, Please help me in this regard

[Chris Martin]

I need the formula

Answer 1

[Torsten]

If you have the statistics toolbox, use nlinfit together with nlparci and nlpredci.

Best wishes

Torsten.

[Chris Martin]

No I have used my own matlab code

[Torsten]

Then you will have to consult the literature cited for nlparci and nlpredci on how confidence intervals for the parameters are to be computed.

See e.g.

http://onlinelibrary.wiley.com/book/10.1002/0471725315

Best wishes

Torsten.

[Chris Martin]

There is nothing in that link

[Torsten]

Just wanted to give a link to this book:

http://www.amazon.com/Nonlinear-Regression-George-F-Seber/dp/0471471356/ref=sr_1_2?ie=UTF8&qid=1446721830&sr=8-2&keywords=Seber+wild

Best wishes

Torsten.

Answer 2

[chris]

You can use Laplace's approximation.

After Levenberg Marquardt (LM) has converged, take the (negative of the) Hessian at that point. This is equal to the precision matrix (inverse of covariance matrix) for a multivariate Gaussian distribution over your parameters.

The location parameter of this distribution is of course just the solution provided by LM.

Note that you do not want to approximate the Hessian with the Jacobian!