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Given sparse or low-quality radial-velocity measurements of a star, there areoften many qualitatively different stellar or exoplanet companion orbit modelsthat are consistent with the data. The consequent multimodality of thelikelihood function leads to extremely challenging search, optimization, andMCMC posterior sampling over the orbital parameters. Here we create a customMonte Carlo sampler for sparse or noisy radial-velocity measurements oftwo-body systems that can produce posterior samples for orbital parameters evenwhen the likelihood function is poorly behaved. The six standard orbitalparameters for a binary system can be split into four non-linear parameters(period, eccentricity, argument of pericenter, phase) and two linear parameters(velocity amplitude, barycenter velocity). We capitalize on this by building asampling method in which we densely sample the prior pdf in the non-linearparameters and perform rejection sampling using a likelihood functionmarginalized over the linear parameters. With sparse or uninformative data, thesampling obtained by this rejection sampling is generally multimodal and dense.With informative data, the sampling becomes effectively unimodal but toosparse: in these cases we follow the rejection sampling with standard MCMC. Themethod produces correct samplings in orbital parameters for data that includeas few as three epochs. The Joker can therefore be used to produce propersamplings of multimodal pdfs, which are still informative and can be used inhierarchical (population) modeling. We give some examples that show how theposterior pdf depends sensitively on the number and time coverage of theobservations and their uncertainties.

The Joker: A custom Monte Carlo sampler for binary-star and exoplanet radial velocity data