2020-08-06

you can never get rid of those spurious modes

It was great to talk to Winston Harris (MTSU) about his results today running The Joker on exoplanet extreme-precision radial-velocity data. Instead of using The Joker to rejection-sample a huge prior sampling of models, he used it just to importance sample or weight each prior sample with the likelihood. In the highly-informative-data regime, rejection sampling only leaves samples in the dominant posterior mode. But importance samplings can be visualized to show all the other modes. His visualization confirms something we (Price-Whelan, Foreman-Mackey, and I) have been saying for years: When you have very informative time-domain data, you don't get a uni-modal likelihood (or posterior): You just get a likelihood (or posterior) with one very dominant mode. Locally, and at very low likelihood, all those other modes still exist. Period-finding is always an extremely non-convex problem.

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