  We perform a comprehensive exploration of the Constrained MSSM parameters
using a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute
superpartner masses and other collider observables as well as a cold dark
matter abundance, and compare them with experimental data. We include
uncertainties arising from theoretical approximations as well as from residual
experimental errors on relevant SM parameters. We delineate probability
distributions of the CMSSM parameters, the collider and cosmological
observables as well as a dark matter direct detection cross section. The 68%
probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26
TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6.
Generally, large fractions of high probability ranges of the superpartner
masses will be probed at the LHC. We highlight a complementarity between LHC
and WIMP dark matter searches in exploring the CMSSM parameter space. We
further expose a number of correlations among the observables, in particular
between BR(B_s \to \mu^+ \mu^-) and BR({\bar B}\to X_s\gamma) or sigma_p^{SI}.
Once SUSY is discovered, this and other correlations may prove helpful in
distinguishing the CMSSM from other supersymmetric models. The robustness of
our results is investigated in terms of the assumed ranges of CMSSM parameters
and the effect of the (g-2)_mu anomaly which shows some tension with the other
observables. We find that the results for m_0, and the observables which
strongly depend on it, are sensitive to our assumptions, while our conclusions
for the other variables are robust.
