Nonlinear fit with constraints in R2012b

Hi,

Is it possible to get parameter estimation variances after constrained optimization?

I am now using lsqnonlin function to optimize 7 parameters with 14 target values, using 'trust-region-reflective' algorithm.

I referred to the following threads, but they seems like mentioning on unconstrained optimizations. http://www.mathworks.com/matlabcentral/answers/51136 http://www.mathworks.com/matlabcentral/answers/45232 http://www.mathworks.com/matlabcentral/newsreader/view_thread/314454

Thanks in advance

[Matt J]

The threads you've referenced refer to parameter estimation variances, not parameter estimation errors. To calculate errors, you need to know their true values. I'll assume you really mean the former.

[Kenta Yoshida]

Thanks Matt, I corrected my question. As you guessed, what I wanted to refer to was parameter estimation variances.

Answer 1

[Matt J]

If none of the constraints are active at your solution, you can estimate the variances in the unconstrained way.

Otherwise, since it's a pretty small problem, why not just estimate the parameter variance by running Monte Carlo simulations?

[Kenta Yoshida]

I'd like to perform Monte Carlo way to estimate parameter variations.

Could you teach me some references for the actual procedure (e.g. how to prepare random samples/ how to express obtained values)? Since I have little background in this field, even basic instructions might work.

Thanks

[José-Luis]

Monte Carlo simulations on 7 parameters with 14 parameters values is still a bit more than 100 million simulations. Whether it's feasible or not depend on how long it takes to run a single simulation.

[Matt J]

I assume "14 parameter values" means that the residuals are in R^14. I hope Kenta doesn't mean that the parameters are discrete-valued. That would make lsqnonlin fairly ineffective.

[Kenta Yoshida]

I meant that the residuals are in R^14, and the parameters are continuous values.

[Matt J]

Anyway, what I was picturing for the simulations was that you assume the parameter estimates given by lsqnonlin are the true values. Then simulate the system measurements with as realistic measurement noise as you can. Then rerun lsqnonlin on these measurements. Do that repeatedly until you have enough data to approximate the variance well.

[Kenta Yoshida]

Thanks a lot again. I will perform that kind of calculation based on the optimized parameter values.