Posterior probability densities for the parameters of the five-planet model for Kepler-139, fitted to the TTVs and RVs. Black contours denote the 0.5σ, 1.0σ, 1.5σ, and 2.0σ joint confidence levels, and 1D histograms show the marginalized distributions. To make this figure of manageable size, we omitted the eccentricity parameters and the periods and mean longitudes of the three transiting planets; the median values and uncertainties for those parameters are reported in Table 1.