An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data .
The periodogram is powered by a parallel tempering MCMC algorithm which is capable of efficiently exploring a multi-planet model parameter space .
The periodogram employs an alternative method for converting the time of an observation to true anomaly that enables it to handle much larger data sets without a significant increase in computation time .
Improvements in the periodogram and further tests using data from HD 208487 have resulted in the detection of a second planet with a period of 909 _ { -92 } ^ { 82 } d , an eccentricity of 0.37 _ { -0.20 } ^ { 0.26 } , a semi-major axis of 1.87 _ { -0.14 } ^ { 0.13 } AU and an M \sin i = 0.45 _ { -0.11 } ^ { 0.13 } M _ { J } .
The revised parameters of the first planet are period = 129.8 \pm 0.4 d , eccentricity = 0.20 \pm 0.09 , semi-major axis = 0.51 \pm 0.02 AU and M \sin i = 0.41 \pm 0.05 M _ { J } .
Particular attention is paid to several methods for calculating the model marginal likelihood which is used to compare the probabilities of models with different numbers of planets .