  Propagation of charged cosmic-rays in the Galaxy depends on the transport
parameters, whose number can be large depending on the propagation model under
scrutiny. A standard approach for determining these parameters is a manual
scan, leading to an inefficient and incomplete coverage of the parameter space.
We implement a Markov Chain Monte Carlo (MCMC), which is well suited to
multi-parameter determination. Its specificities (burn-in length, acceptance,
and correlation length) are discussed in the phenomenologically well-understood
Leaky-Box Model. From a technical point of view, a trial function based on
binary-space partitioning is found to be extremely efficient, allowing a
simultaneous determination of up to nine parameters, including transport and
source parameters, such as slope and abundances. Our best-fit model includes
both a low energy cut-off and reacceleration, whose values are consistent with
those found in diffusion models. A Kolmogorov spectrum for the diffusion slope
(delta=1/3) is excluded. The marginalised probability-density function for
delta and alpha (the slope of the source spectra) are delta~0.55-0.60 and
alpha~2.14-2.17, depending on the dataset used and the number of free
parameters in the fit. All source-spectrum parameters (slope and abundances)
are positively correlated among themselves and with the reacceleration
strength, but are negatively correlated with the other propagation parameters.
A forthcoming study will extend our analysis to more physical diffusion models.
