  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$_{\rm J}$.
The revised parameters of the first planet are period $= 129.8\pm 0.4$d,
eccentricity $= 0.20\pm 0.09$, semi-major axis $= 0.51\pm0.02$ AU and $M \sin i
= 0.41\pm0.05$ M$_{\rm J}$. 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.
