constant. We incorporate  into our analysis to sample the probability distribution function within a Bayesian framework. A significant advantage of this is that the results are presented as posterior probability distribution functions, which indicate parameter correlations and provide more robust uncertainty estimates.

 explores the parameter space using a set of walkers, in our case 142. These chains begin with a uniform prior probability distribution for each parameter. At every iteration, each chain assesses its likelihood with respect to that of another chain and then elects whether to move towards that chain. The new parameters are based on the covariance matrix of the two chains. If the move increases the posterior likelihood then it is accepted; if the move decreases it then it may be accepted with a certain probability. During the initial burn-in time, Markov chains are converging towards their maximum likelihood position. The statistics of a large number of iterations provide converged posterior distributions for the model parameters.

We create a model of all available data (light curves and radial velocities) for each binary star. To assess convergence, we use auto-correlation timescales. The auto-correlation timescale is used to estimate the number of iterations required to generate an independent sample, 