  We apply a Bayesian data analysis scheme known as the Markov Chain Monte
Carlo (MCMC) to the tomographic reconstruction of quantum states. This method
yields a vector, known as the Markov chain, which contains the full statistical
information concerning all reconstruction parameters including their
statistical correlations with no a priori assumptions as to the form of the
distribution from which it has been obtained. From this vector can be derived,
e. g. the marginal distributions and uncertainties of all model parameters and
also of other quantities such as the purity of the reconstructed state. We
demonstrate the utility of this scheme by reconstructing the Wigner function of
phase-diffused squeezed states. These states posses non-Gaussian statistics and
therefore represent a non-trivial case of tomographic reconstruction. We
compare our results to those obtained through pure maximum-likelihood and
Fisher information approaches.
