Extra-solar Planets via Bayesian Fusion MCMC This manuscript to appear as Chapter 7 in ‘Astrostatistical Challenges for the New Astronomy’, Springer Series in

Abstract A Bayesian multi-planet Kepler periodogram has been developed based on a fusion Markov chain Monte Carlo algorithm (FMCMC). FMCMC is a new general purpose tool for nonlinear model fitting. It incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features fa-cilitate the detection of a global minimum in chi-squared in a highly multi-modal environment. By combining all three, the algorithm greatly increases the probability of realizing this goal. The FMCMC is controlled by a unique adaptive control system that automates the tuning of the proposal distributions for efficient exploration of the model param-eter space even when the parameters are highly correlated. This controlled statisti-cal fusion approach has the potential to integrate other relevant statistical tools as desired. The FMCMC algorithm is implemented in Mathematica using parallized code and run on an 8 core PC. The performance of the algorithm is illustrated with some recent successes in the exoplanet field where it has facilitated the detection of a number of new planets. Bayesian model selection is accomplished with a new method for computing marginal likelihoods called Nested Restricted Monte Carlo (NRMC).