• DOI:10.1111/j.1365-2966.2009.16233.x
• Corpus ID: 16722873

A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris

@article{Gregory2010ABP,
  title={A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris},
  author={Philip C. Gregory and Debra A. Fischer},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2010},
  volume={403},
  pages={731-747}
}

• P. Gregory, D. Fischer
• Published 29 March 2010
• Physics, Geology
• Monthly Notices of the Royal Astronomical Society

A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325 days. The analysis also provides orbital constraints on an additional long period planet with a period � 10000 days. The three planet model is found to be 10 5 times more probable than the next most probable model which is a two planet model. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features facilitate the detection of a global minimum in � 2 . By combining all three, the HMCMC greatly increases the probability of realizing this goal. When applied to the Kepler problem it acts as a powerful multiplanet Kepler periodogram. The measured periods are 1078 ± 2, 2391 +100 87 , and 14002 [phone] d, and the corresponding eccentricities are 0:032 ± 0:014, 0:098 +.047 .096 , and 0:16