  Research in many areas of modern physics such as, e.g., indirect searches for
dark matter and particle acceleration in SNR shocks, rely heavily on studies of
cosmic rays (CRs) and associated diffuse emissions (radio, microwave, X-rays,
gamma rays). While very detailed numerical models of CR propagation exist, a
quantitative statistical analysis of such models has been so far hampered by
the large computational effort that those models require. Although statistical
analyses have been carried out before using semi-analytical models (where the
computation is much faster), the evaluation of the results obtained from such
models is difficult, as they necessarily suffer from many simplifying
assumptions, The main objective of this paper is to present a working method
for a full Bayesian parameter estimation for a numerical CR propagation model.
For this study, we use the GALPROP code, the most advanced of its kind, that
uses astrophysical information, nuclear and particle data as input to
self-consistently predict CRs, gamma rays, synchrotron and other observables.
We demonstrate that a full Bayesian analysis is possible using nested sampling
and Markov Chain Monte Carlo methods (implemented in the SuperBayeS code)
despite the heavy computational demands of a numerical propagation code. The
best-fit values of parameters found in this analysis are in agreement with
previous, significantly simpler, studies also based on GALPROP.
