We explore a method to extract energy eigenstates, called Athens Model Independent Analysis Scheme (AMIAS),
which is an alternative to solving standard Generalized Eigenvalue Problems (GEVP). The method is based on statistically
sampling the space of fit parameters according to the $\chi^2$ value of the fit function. The method is particularly
suited for correlators or correlation matrices with strong contributions from several energy eigenstates and for rather
noisy data, e.g. for correlators with disconnected or partly disconnected diagrams. We apply the method to the analysis
of the $J^P = 0^+$ channel in the context of our investigation of the $a_0(980)$ meson and point out advantages compared to the GEVP.