Fig. 7.

Plot of the acceptance fraction f_Acc (green) and average minimum goodness of fit value converged towards with standard uncertainty (black) for several MCMC algorithm runs at different σ_Step sizes. Uncertainty bars are standard uncertainty for 96 chains. The minimum goodness of fit value converged towards occurred around σ_Step ≅ 32. Here the objective function Ξ was used and normalized by the number Ξ_Norm to get the data comparable with the acceptance fractions (i.e. Ξ_Norm converts the goodness of fit value to arbitrary scaled units; a value of Ξ_Norm =3578 was used). At large σ_Step, the algorithm accepts many parameter set moves and thus works poorly. Conversely, at small σ_Step, the parameter set moves result in almost no acceptance events and the algorithm also works poorly. Thus the medium value of σ_Step = 32 where Ξ was minimized was used in further MCMC runs.