Posterior distributions of LG properties from our Markov chains. In each panel, the histogram is of samples from our chains and therefore indicates the posterior distribution. The dashed lines are the injected observational constraints. The top left panel indicates the centre-of-mass position of the Milky Way, and the top middle panel M31. The right panel shows the relative velocity of the MW-M31 pair. The bottom left and middle panels indicate the 100 kpc filtered masses of the Milky Way and M31. The bottom right panel shows the total log-likelihood of the flow tracers, with on top the χ²-distribution (scaled by $-\frac{1}{2}$, since the log-likelihood is −χ²/2). These histograms are of the ‘semi-independent’ set of simulations as described in Section 3.3.