We present the results of a realistic global fit of the Lagrangian parameters of the Minimal Supersymmetric Standard Model to simulated data from ILC and LHC with realistic estimates of the observable uncertainties. Higher order radiative corrections are accounted for where ever possible to date. Results are obtained for a modified SPS1a MSSM benchmark scenario but they were checked not to depend critically on this assumption. Exploiting a simulated annealing algorithm, a stable result is obtained without any a priori assumptions on the fit parameters. Most of the Lagrangian parameters can be extracted at the percent level or better if theoretical uncertainties are neglected. Neither LHC nor ILC measurements alone will be sufficient to obtain a stable result. The effects of theoretical uncertainties arising from unknown higher-order corrections and parametric uncertainties are examined qualitatively. They appear to be relevant and the result motivates further precision calculations.
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