Fitting Issues
Genetic Algorithm.A major problem when fitting complex models is that the fit can stop at a local minimum. Most optimization techniques are local and cannot guard against this possibility.
A popular global optimization technique is use of a genetic algorithm. This attempts to mimic evolution by natural selection (which supposedly optimizes a species' chances of survival). The way this works in the context of XSPEC is that sets of model parameters can be considered as individuals and their survival fitness is how well the model fits the data.
The sets of model parameters are "bred" over many generations with those that provide the best fit to the data passing their genome onto the next generation. This algorithm is slow but sure. One advantage is that the result is a population of good fits. These can be examined to check that they cluster in one region of parameter space.
In conventional spectral fitting all the uncertainty is assumed to reside in the data points. However, models can have uncertainty too. Inadequate knowledge of atomic physics means detailed plasma models (both collisional and photo-ionized) have uncertainties. Models based on Monte Carlo calculations are limited by the number of realizations computed.
We have modified XSPEC to allow models to have errors associated with each energy bin. These errors are added in quadrature to those on the data and used in the chi-squared statistic. We plan to also allow errors to be associated with the instrument response to reflect uncertainties in the calibration.