We study the properties of the constrained minimal supersymmetric standard
model (mSUGRA) by performing fits to updated indirect data, including the relic
density of dark matter inferred from WMAP5. In order to find the extent to
which mu 0, we compare the Bayesian
evidence values for these models, which we obtain straightforwardly and with
good precision from the recently developed multi-modal nested sampling
('MultiNest') technique. We find weak to moderate evidence for the mu > 0
branch of mSUGRA over mu < 0 and estimate the ratio of probabilities to be P(mu
> 0)/P(mu < 0) = 6-61 depending on the prior measure and range used. There is
thus positive (but not overwhelming) evidence that mu > 0 in mSUGRA. The
MultiNest technique also delivers probability distributions of parameters and
other relevant quantities such as superpartner masses. We explore the
dependence of our results on the choice of the prior measure used. We also use
the Bayesian evidence to quantify the consistency between the mSUGRA parameter
inferences coming from the constraints that have the largest effects: (g-2)_mu,
BR(b -> s gamma) and cold dark matter (DM) relic density Omega_{DM}h^2.Comment: 28 pages, 8 figures, minor revision, accepted for publication in JHE
