Posterior inference for two example binary systems using our forward-modelling approach: a luminous stellar binary (DR3 4609711364265062016, left panels) and a compact-object binary, Gaia BH 2 (DR3 5870569352746779008, right panels). Top row: Posterior samples in the space of companion mass vs orbital period, along with the marginalised posterior distribution of the companion mass. The orange star symbols mark the true (injected) parameters of each system; the blue stars denote the inferred best-fit parameters (posterior-weighted mean). The dashed ellipses indicate the 1σ and 2σ confidence contours derived from the covariance matrix. Bottom row: Predicted observables (ruwe vs RV uncertainty σ_RV) for the same posterior samples, colour-coded by the companion mass. The observed values are again shown as orange stars. In the stellar case, the low-mass companions reproduce the observed signatures well; in the BH case, a high companion mass is required to explain the elevated ruwe and moderate σ_RV, consistent with the true binary configurations. Much of the variance in predicting the observables results from the random sampling of RV epochs, which can produce varying observables also for the same binary parameters.