Panel a: posterior distributions of the orbital period P_b of the injected planet for some selected mock datasets. The histogram in green corresponds to a dataset for which P_b has been recovered with high precision and accuracy. The posterior in blue corresponds to a case with a very accurate but less precise retrieved P_b, and the posterior in red corresponds to a mock dataset for which the orbital period was not recovered. Panel b: distribution of the P_{b, retrieved}/P_{b, inj} ratio between the median best-fit orbital period and the injected value for each simulated dataset. Panel c: same as for panel b, but using the values of P_b corresponding to the MAP estimates. Panel d: distribution of the significance of the retrieved best-fit values P_b for the S₃₂ sub-sample described in the text. The significance is expressed as the ratio between the median of the posterior and the corresponding lower uncertainty for each simulated dataset. Panel e: distribution of the ratio between the recovered and injected semi-amplitude K_b of the planetary RV signal for the 32% of the simulated datasets for which an accurate and precise estimate of P_b was recovered (S₃₂ sample). Panel f: results of a model comparison analysis. The plot shows the distribution of the difference -, calculated for the 100 mock RV datasets, between the Bayesian evidence of the model including one sinusoid (i.e. one planet on a circular orbit) and the model with only a GP-term. The model including one planet is marginally more significant (-2) only in two cases, one being that corresponding to the posterior of P_b in green shown in panel a.