Authors:Damasso et alAbstract:The detection and characterization 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-analyze the radial velocity data that led to the detection of a candidate terrestrial planet orbiting the star Proxima Centauri. We aim at confirming the existence of this outstanding planet, and test the existence of a second planetary signal. Our technique jointly models Keplerian signals and residual correlated signals (the noise) in radial velocities using Gaussian Processes. We analyse only radial velocity measurements without including other ancillary data. In a second step, we compare our outputs with results coming from photometry, to provide a consistent physical interpretation. Our analysis is performed in a Bayesian framework to quantify the robustness of our findings. We show that the correlated noise can be successfully modeled as a Gaussian process regression. It contains a periodic term modulated on the stellar rotation period and characterized by an evolutionary timescale of the order of 1 year. Both findings appear to be robust when compared with results obtained from archival photometry. We confirm the existence of a coherent signal described by a Keplerian orbit equation that can be attributed to the planet Proximab, and provide an independent estimate of the planetary parameters. Our Bayesian analysis dismisses the existence of a second planetary signal in the present dataset.