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tokens: from stellar activity). The likelihood function is given by where i indexes the observations acquired with the I th instrument, is the nominal uncertainty of each RV measurement, and s I are the zero-point and extra noise parameters (also called jitter) of each instrument, and the Doppler signal from a companion on the star is encoded in the model , which is a function of time t and the Keplerian parameters . The Keplerian parameters of the p th companion in the system are: the orbital period P p (in days), the semi-amplitude K p (in m s −1 ), the mean anomaly at the reference epoch t 0 (in degrees), the eccentricity e p , and the argument of periastron . The second and third terms in Equation ( 3 ) account for the possible presence of a long-period candidate whose orbit is only detected as a trend (acceleration, ) plus some curvature (jerk, ). These two terms are especially important for the analysis that follows. When performing the Bayesian MCMC analysis, one needs to specify some prior distributions for these parameters. In this paper, we use uniform distributions for the angles and ω , as any value would be equally likely a priori. Given that the objects involved are rather massive and the signals are large, we also allow for a uniform eccentricity distribution between [0,0.95). For K p , , s I , , and , we assume unbound non-normalized uniform priors. While this can cause issues when normalizing the posterior, we are only using the MCMC analysis to sample the shape of the posterior, so precise values of the bounds and the normalization factors are unnecessary. Furthermore, because we will later try to constrain the signal with a period much longer than the span of the observations, the possible values of these three quantities will be correlated, so bound priors might eliminate many long period solutions that would otherwise be highly probable. For example, a large K in general requires a large γ unless the companion is precisely crossing the plane of the sky at t 0 (which is highly unlikely). Regarding the prior on the period, in this work we assume that the prior is uniform in (equivalent to uniform in frequency). This is motivated by the following. When analyzing time series, the local solutions to periodic signals are approximately equally spaced in frequency. For example, if one produces a Lomb–Scargle periodogram of a time series and plots period versus power, one will quickly appreciate that the peaks become much broader with increasing period (Scargle 1982 ). However, when making the same plot in frequency, the peaks appear uniformly distributed over the possible frequencies. As discussed in Tuomi and Anglada-Escudé ( 2013 ), in Bayesian statistics the choice of the parameter automatically imposes implicit priors on all other alternative parameterizations. In the case of the period, a uniform prior at very long periods can outweigh the information content on the likelihood, producing a biased result. While this issue