Fast Bayesian Inference for Exoplanet Discovery in Radial Velocity Data

TL;DR

This paper introduces a trans-dimensional Bayesian inference method using Nested Sampling to efficiently determine the number of exoplanets from radial velocity data, even with complex, multimodal posteriors.

Contribution

It presents a novel approach combining trans-dimensional MCMC with Nested Sampling to infer the number of planets and their parameters in a single analysis.

Findings

Detected multiple signals in $ u$ Oph with high posterior probability.

Identified many potential planets in Gliese 581, with some having well-determined periods.

Demonstrated the presence of phase transitions that challenge traditional sampling methods.

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 trans-dimensional 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 $\nu$ Oph and Gliese 581, finding moderate evidence for additional signals in $\nu$ Oph with periods of 36.11 $\pm$ 0.034 days, 75.58 $\pm$ 0.80 days, and 1709 $\pm$ 183 days; the posterior probability that at least one of these exists is 85%. The results also suggest Gliese 581 hosts many (7-15) "planets" (or other causes of other periodic signals), but only 4-6 have well determined periods. The analysis of both of these datasets shows phase transitions exist which are difficult to negotiate without Nested Sampling.