Minimization of Chi-Square Statistic using the Simplex Algorithm

Hi,

I am working on a model fitting project in which I want to estimate the best fitting parameters of my computational model (3 key parameters of interest) using the chi-square goodness of fit test and to do so want to minimize the chi-square statistic for parameter estimation, using the simplex optimisation algorithm. Can some one help me by explaining how we can perform this in Matlab? Can we use the optimisation toolbox GUI for it? if so how (or where can I find the instructions)?

Secondly, are there any other parameter optimization algorithms we could use for such model fitting and best fit parameter estimation processes, when using chi-square goodness of fit?

Thanks in advance for your help!

Answer 1

[Jeff Miller]

One way to proceed is to write a function which accepts a vector of values for your three parameters, and returns the chi-square value computed using those parameter values. Then you use fminsearch to minimize that function. fminsearch will try different values of the parameter values and do the best it can to minimize the value of chi-square. There are no guarantees of finding the best parameter values this way, but it is a common approach when it is too hard to minimize the chi-square mathematically.

There are other methods too, but fminsearch is usually the simplest. Look here for a little more detail.