Context : 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 .

Aims : In analyzing the data from forthcoming experiments , a more sophisticated strategy is required .
An automated statistical tool is used , which enables a full coverage of the parameter space and provides a sound determination of the transport and source parameters .
The uncertainties in these parameters are also derived .

Methods : 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 context of cosmic-ray physics .
Its capabilities and performances are explored in the phenomenologically well-understood Leaky-Box Model .

Results : 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 \approx 0.55 - 0.60 and \alpha \approx 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 .

Conclusions : The MCMC is a practical and powerful tool for cosmic-ray physic analyses .
It can be used to confirm hypotheses concerning source spectra ( e.g. , whether \alpha _ { i } \neq \alpha _ { j } ) and/or determine whether different datasets are compatible .
A forthcoming study will extend our analysis to more physical diffusion models .