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We present statistically convergent profile likelihood maps obtained viaglobal fits of a phenomenological Minimal Supersymmetric Standard Model with 15free parameters (the MSSM-15), based on over 250M points. We derive constraintson the model parameters from direct detection limits on dark matter, the Planckrelic density measurement and data from accelerator searches. We provide adetailed analysis of the rich phenomenology of this model, and determine theSUSY mass spectrum and dark matter properties that are preferred by currentexperimental constraints. We evaluate the impact of the measurement of theanomalous magnetic moment of the muon ($g-2$) on our results, and provide ananalysis of scenarios in which the lightest neutralino is a subdominantcomponent of the dark matter. The MSSM-15 parameters are relatively weaklyconstrained by current data sets, with the exception of the parameters relatedto dark matter phenomenology ($M_1$, $M_2$, $\mu$), which are restricted to thesub-TeV regime, mainly due to the relic density constraint. The mass of thelightest neutralino is found to be < 1.5 TeV at 99% C.L., but can extend up to3 TeV when excluding the $g - 2$ constraint from the analysis. Low-massbino-like neutralinos are strongly favoured, with spin-independent scatteringcross-sections extending to very small values, $\sim 10^{-20}$ pb. ATLAS SUSYnull searches strongly impact on this mass range, and thus rule out a region ofparameter space that is outside the reach of any current or future directdetection experiment. The best-fit point obtained after inclusion of all datacorresponds to a squark mass of 2.3 TeV, a gluino mass of 2.1 TeV and a 130 GeVneutralino with a spin-independent cross-section of $2.4 \times 10^{-10}$ pb,which is within the reach of future multi-ton scale direct detectionexperiments and of the upcoming LHC run at increased centre-of-mass energy.

Profile likelihood maps of a 15-dimensional MSSM