  Previous LHC forecasts for the constrained minimal supersymmetric standard
model (CMSSM), based on current astrophysical and laboratory measurements, have
used priors that are flat in the parameter tan beta, while being constrained to
postdict the central experimental value of MZ. We construct a different, new
and more natural prior with a measure in mu and B (the more fundamental MSSM
parameters from which tan beta and MZ are actually derived). We find that as a
consequence this choice leads to a well defined fine-tuning measure in the
parameter space. We investigate the effect of such on global CMSSM fits to
indirect constraints, providing posterior probability distributions for Large
Hadron Collider (LHC) sparticle production cross sections. The change in priors
has a significant effect, strongly suppressing the pseudoscalar Higgs boson
dark matter annihilation region, and diminishing the probable values of
sparticle masses. We also show how to interpret fit information from a Markov
Chain Monte Carlo in a frequentist fashion; namely by using the profile
likelihood. Bayesian and frequentist interpretations of CMSSM fits are compared
and contrasted.
