  The Gliese 581 planetary system has received attention because it has been
proposed to host a low-mass planet in its habitable zone. We re-analyse the
radial velocity measurements reported to contain six planetary signals to see
whether these conclusions remain valid when the analyses are made using
Bayesian tools instead of the common periodogram analyses. We analyse the
combined radial velocity data set obtained using the HARPS and HIRES
spectrographs using posterior sampling techniques and computation of the
posterior probabilities of models with differing numbers of Keplerian signals.
We do not fix the orbital eccentricities and stellar jitter to certain values
but treat these as free parameters of our statistical models. Hence, we can
take the uncertainties of these parameters into account when assessing the
number of planetary signals present in the data, the point estimates of all of
the model parameters, and the uncertainties of these parameters. We conclude
that based on the Bayesian model probabilities and the nature of the posterior
densities of the different models, there is evidence in favour of four planets
orbiting GJ 581. The HARPS and HIRES data do not imply the conclusion that
there are two additional companions orbiting GJ 581. We also revise the orbital
parameters of the four companions in the system. Especially, according to our
results, the eccentricities of all the companions in the system are consistent
with zero.
