  Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference
and in particular for exoplanet radial velocity fitting because MCMC provides
more statistical information and makes better use of data than common
approaches like chi-square fitting. However, the non-linear density functions
encountered in these problems can make MCMC time-consuming. In this paper, we
apply an ensemble sampler respecting affine invariance to orbital parameter
extraction from radial velocity data. This new sampler has only one free
parameter, and it does not require much tuning for good performance, which is
important for automatization. The autocorrelation time of this sampler is
approximately the same for all parameters and far smaller than
Metropolis-Hastings, which means it requires many fewer function calls to
produce the same number of independent samples. The affine-invariant sampler
speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the
same computing situation. This novel sampler would be ideal for projects
involving large datasets such as statistical investigations of planet
distribution. The biggest obstacle to ensemble samplers is the existence of
multiple local optima; we present a clustering technique to deal with local
optima by clustering based on the likelihood of the walkers in the ensemble. We
demonstrate the effectiveness of the sampler on real radial velocity data.
