Optimizing 2D Data Models: Best Routines for X & Error

[natski]

Dear all,

I am looking for some advise on optimization routines. I have a collection of 2D data (x-y plot) and a piece of code which generates different models based upon several inputs (a,b,c,d,etc). These inputs generate several outputs which characterize the final generated model (x,y,z...).

I wish to find the optimum value in just one characterizing parameter, say x, plus a very careful and precise value for the error in x.

The simplest thing to do would be a chi squared minimization and then allow chi-squared to change by +1 to get the upper and lower limits on x, but I don't think this is really the best.

A more advanced approach would be to use a Markov Chain Monte Carlo (MCMC) method. Or maybe I should use a hybrid Hamiltonian MCMC algorithm (is this better?).

Another option is genetic algorithms...

What, in your experience, is a reasonably easy to implement, exact and precise, but not computationally too demanding, method to find the value of x and error?

Thanks,

nastski

 

[PhysicsDruid]

Along the same lines of Chi Squares and Monte Carlos... in general, matters of this sort are done through Likelihood calculations.

Are you familiar with the freely available software called ROOT ? This has a MINUIT routine in its structure that may be useful for you, as well as, already available classes that you may be able to inherit easily from to represent your own function and then pass it as a parameter, then letting MINUIT determine the best fit parameters.

Hopefully my reply hasn't come a day too late.Edit: I believe this should be moved to the programming thread?