  The detection and characterisation of Earth-like planets with Doppler signals
of the order of 1 m/s currently represent one of the greatest challenge for
extrasolar-planet hunters. As results for such findings are often
controversial, it is desirable to provide independent confirmations of the
discoveries. Testing different models for the suppression of non-Keplerian
stellar signals usually plaguing radial velocity data is essential to ensuring
findings are robust and reproducible. Using an alternative treatment of the
stellar noise to that discussed in the discovery paper, we re-analyse the
radial velocity dataset that led to the detection of a candidate terrestrial
planet orbiting the star Proxima Centauri. We aim to confirm the existence of
this outstanding planet, and test the existence of a second planetary signal.
Our technique jointly modelled Keplerian signals and residual correlated
signals in radial velocities using Gaussian processes. We analysed only radial
velocity measurements without including other ancillary data in the fitting
procedure. In a second step, we have compared our outputs with results coming
from photometry, to provide a consistent physical interpretation. Our analysis
was performed in a Bayesian framework to quantify the robustness of our
findings. We show that the correlated noise can be successfully modelled as a
Gaussian process regression, and contains a periodic term modulated on the
stellar rotation period and characterised by an evolutionary timescale of the
order of one year. Both findings appear to be robust when compared with results
obtained from archival photometry, thus providing a reliable description of the
noise properties. We confirm the existence of a coherent signal described by a
Keplerian orbit equation that can be attributed to the planet Proxima b [...]
