Today's research highlight was our weekly MCMC meeting, which included Brewer and Schölkopf in addition to the regulars Goodman, Hou, Foreman-Mackey, and Fadely. We discussed many matters, including but not limited to: how to make use of rejected samples (that is, how to not waste those likelihood calls which resulted in samples that are not in the output chain), how to replace MCMC with a method that returns something better than a mixture-of-delta-functions approximation for the posterior, how to combine MCMC with classification or other machine-learning methods to turn a multi-modal posterior into a mixture of uni-modal distributions, and how to propagate errors in diffusive nested sampling and how to make that method more adaptive. Hou has some results on exoplanets in which some stars (radial velocity data here) have roughly similar marginalized likelihood (Bayesian evidence) for two-planet and three-planet models. We discussed how to diagnose these situations. Brewer predicted that if the evidence is good, then the parameters should also be well constrained. That also jives with my intuitions. We encouraged Hou to make visualizations and predictions; some of these cases might turn into discoveries.