Fast Bayesian inference for exoplanet discovery in radial velocity data
Abstract
Inferring the number of planets N in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to distinguish from planetary signals. However, even doing the inference under a given set of simplifying assumptions (e.g. no stellar activity) can be difficult. It is common for the posterior distribution for the planet parameters, such as orbital periods, to be multimodal and to have other awkward features. In addition, when N is unknown, the marginal likelihood (or evidence) as a function of N is required. Rather than doing separate runs with different trial values of N, we propose an alternative approach using a transdimensional Markov Chain Monte Carlo method within nested sampling. The posterior distribution for N can be obtained with a single run. We apply the method to ν Oph and Gliese 581, finding moderate evidence for additional signals in ν Oph with periods of 36.11 ± 0.034, 75.58 ± 0.80, and 1709 ± 183 d; the posterior probability that at least one of these exists is 85 per cent. The results also suggest Gliese 581 hosts many (715) `planets' (or other causes of other periodic signals), but only 46 have well determined periods. The analysis of both of these data sets shows phase transitions exist which are difficult to negotiate without nested sampling.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2015
 DOI:
 10.1093/mnras/stv199
 arXiv:
 arXiv:1501.06952
 Bibcode:
 2015MNRAS.448.3206B
 Keywords:

 methods: data analysis;
 methods: statistical;
 techniques: radial velocities;
 planetary systems;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Earth and Planetary Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability;
 Statistics  Applications
 EPrint:
 Accepted for publication in MNRAS. 9 pages, 12 figures. Code at http://www.github.com/eggplantbren/Exoplanet