  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.
