  The start of LHC has motivated an effort to determine the relative
probability of the different regions of the MSSM parameter space, taking into
account the present, theoretical and experimental, wisdom about the model.
Since the present experimental data are not powerful enough to select a small
region of the MSSM parameter space, the choice of a judicious prior probability
for the parameters becomes most relevant. Previous studies have proposed
theoretical priors that incorporate some (conventional) measure of the
fine-tuning, to penalize unnatural possibilities. However, we show that such
penalization arises from the Bayesian analysis itself (with no ad hoc
assumptions), upon the marginalization of the mu-parameter. Furthermore the
resulting effective prior contains precisely the Barbieri-Giudice measure,
which is very satisfactory. On the other hand we carry on a rigorous treatment
of the Yukawa couplings, showing in particular that the usual practice of
taking the Yukawas "as required", approximately corresponds to taking
logarithmically flat priors in the Yukawa couplings. Finally, we use an
efficient set of variables to scan the MSSM parameter space, trading in
particular B by tan beta, giving the effective prior in the new parameters.
Beside the numerical results, we give accurate analytic expressions for the
effective priors in all cases. Whatever experimental information one may use in
the future, it is to be weighted by the Bayesian factors worked out here.
