star spots in the model for an eclipsing binary star because the number of free parameters required is large and the constraints on these parameters from the light curve are generally weak and highly degenerate. We did not attempt to model star spots for any of the binary systems here since the amplitude of the star spot modulation is generally quite small ($\la 0.5\%$) so the resulting systematic error in the parameters derived will, in general, not be large enough to alter our conclusions regarding the nature of the binary. Instead, we simply divide-out the time trend due to star spot modulation established from the Gaussian process fit to the out-of-eclipse data.

We used [emcee]{} [@2013PASP..125..306F], a [python]{} implementation of an affine invariant Markov chain Monte Carlo (MCMC) ensemble sampler, to calculate the posterior probability distribution of the model parameters. We used an ensemble with at least twice the number samples per chain step (“walkers”) as there were model parameters and 5,000 or 10,000 steps in the chain used for the results quoted below. The convergence of the chain was judged by visual inspection of the parameters and the likelihood as a function of step number. In cases where we 