Orbits for the Impatient: A Bayesian Rejection-sampling Method for Quickly Fitting the Orbits of Long-period Exoplanets

Sarah Blunt, Eric L. Nielsen, Robert J. De Rosa, Quinn M. Konopacky, Dominic Ryan, Jason J. Wang, Laurent Pueyo, Julien Rameau, Christian Marois, Franck Marchis, Bruce Macintosh, James R. Graham, Gaspard Duchêne, Adam C. Schneider

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


We describe a Bayesian rejection-sampling algorithm designed to efficiently compute posterior distributions of orbital elements for data covering short fractions of long-period exoplanet orbits. Our implementation of this method, Orbits for the Impatient (OFTI), converges up to several orders of magnitude faster than two implementations of Markov Chain Monte Carlo (MCMC) in this regime. We illustrate the efficiency of our approach by showing that OFTI calculates accurate posteriors for all existing astrometry of the exoplanet 51 Eri b up to 100 times faster than a Metropolis-Hastings MCMC. We demonstrate the accuracy of OFTI by comparing our results for several orbiting systems with those of various MCMC implementations, finding the output posteriors to be identical within shot noise. We also describe how our algorithm was used to successfully predict the location of 51 Eri b six months in the future based on less than three months of astrometry. Finally, we apply OFTI to 10 long-period exoplanets and brown dwarfs, all but one of which have been monitored over less than 3% of their orbits, producing fits to their orbits from astrometric records in the literature.

Original languageEnglish (US)
Article number229
JournalAstronomical Journal
Issue number5
StatePublished - May 2017


  • methods: statistical
  • planets and satellites: fundamental parameters
  • stars: imaging

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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