Fitting in a complex χ(2) landscape using an optimized hypersurface sampling.

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the χ(2) hypersurface, depending on a set of parameters {P(i)}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global χ(2) hypersurface minimum, jumping across χ(2){P(i)} barriers when necessary, is demonstrated with synthetic functions and with real data.