Context. The detection and characterisation of Earth-like planets with Doppler signals of the order of 1  m s-1 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. Aims. 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. Methods. 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. Results. 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, and provide an independent estimate of the planetary parameters. Our Bayesian analysis dismisses the existence of a second planetary signal in the present dataset.