If new physics is found at the LHC (and the ILC) the reconstruction of the underlying theory should not be biased by assumptions about high--scale models. For the mapping of many measurements onto high--dimensional parameter spaces we introduce SFitter with its new weighted Markov chain technique. SFitter constructs an exclusive likelihood map, determines the best--fitting parameter point and produces a ranked list of the most likely parameter points. Using the example of the TeV--scale supersymmetric Lagrangian we show how a high--dimensional likelihood map will generally include degeneracies and strong correlations. SFitter allows us to study such model--parameter spaces employing Bayesian as well as frequentist constructions. We illustrate in detail how it should be possible to analyze high--dimensional new--physics parameter spaces like the TeV--scale MSSM at the LHC. A combination of LHC and ILC measurements might well be able to completely cover highly complex TeV--scale parameter spaces.
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