Philip C. Gregory

A remarkable array of new ground based and space based astronomical tools are providing astronomers access to other solar systems. Approximately 500 planets have been discovered to date including at least one super earth in the habitable zone of the star Gliese 581. These successes on the part of the observers have spurred a significant effort to improve the statistical tools for analyzing data in this field. Much of the recent work has highlighted a Bayesian MCMC approach as a way to better understand parameter uncertainties and degeneracies and to compute model probabilities.

I will describe a Bayesian multi-planet Kepler periodogram based on a new fusion Markov chain Monte Carlo algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features facilitate the detection of a global minimum in chi-squared in a multi-modal environment. By combining all three, the algorithm greatly increases the probability of realizing this goal.

The fusion MCMC is controlled by a unique two stage adaptive control system that automates the tuning of the proposal distributions for efficient exploration of the model parameter space even when the parameters are highly correlated. The fusion MCMC algorithm is implemented in *Mathematica* using parallized code and run on an 8 core PC. It is designed to be a very general tool for nonlinear model fitting. The performance of the algorithm will be illustrated with some recent successes in the exoplanet field where it has facilitated the detection of a number of new planets.

**Keywords:** Exoplanets; Bayesian inference; MCMC; Kepler multi-planet periodogram

**Biography:** After a successful career in radio astronomy, Phil signed up to teach a graduate physics course on measuremt theory to broaden his horizons. In the process he encountered Bayesian inference and became an immediate convert. In 2005, Cambridge University Press published his text book on the subject: “Bayesian Logical Data Analysis for the Physical Sciences: With Mathematica Support.” Phil has developed a variety of useful Bayesian algorithms the latest of which is a new type of Markov chain Monte Carlo algorithm for Bayesian nonlinear model fitting. He will describe an exciting application of this algorithm to extra-solar planet detection where the algorithm acts as a multi-planet Kepler periodogram.