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

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Chris Martin
Chris Martin 2015-11-4
评论： Star Strider 2015-11-10
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

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Torsten
Torsten 2015-11-4
If you have the statistics toolbox, use nlinfit together with nlparci and nlpredci.
Best wishes
Torsten.
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Star Strider
Star Strider 2015-11-5
Finding the covariance matrix of a nonlinear regression requires that you calculate the Jacobian matrix at the convergence (the last parameter estimates calculated). In the context of the Wikipedia notation, the partial derivatives are with respect to each parameter at each data point, so the partial derivative of f(1) with respect to x(1) refers to the value of the partial derivative of the function at the first value of the independent variable with respect to the first parameter. It continues row-wise down the values of the independent variable, and column-wise across the parameters.
In a nonlinear regression, some or all of the partial derivatives of the function with respect to each parameter are by definition functions of themselves or of other parameters, so expect that in your result. (This is known as the model being ‘nonlinear in the parameters’.) This is easier if you have the Symbolic Math Toolbox, since it can calculate the symbolic Jacobian for you.
After that, you can plug your evaluated Jacobian matrix into the design matrix for a linear problem to calculate the covariance matrix, as explained in Least squares, regression analysis, and statistics. You can calculate the parameter confidence intervals from the diagonals of the covariance matrix and the t-distribution.
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