Mathematics – Probability
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011aas...21734320n&link_type=abstract
American Astronomical Society, AAS Meeting #217, #343.20; Bulletin of the American Astronomical Society, Vol. 43, 2011
Mathematics
Probability
Scientific paper
For single-planet or weakly-interacting planetary systems, Markov chain Monte Carlo (MCMC) and the Metropolis-Hastings algorithm have gained widespread use for interpreting Doppler and transit observations. At least 15 of the 50 extrasolar multi-planet systems appear to be in or near a mean-motion resonance. Some and perhaps most of these systems undergo planet-planet interactions on the observing timescale. Interpreting Doppler observations of such systems requires using self-consistent N-body integrations and exploring a high-dimensional ( 7 x number of planets) parameter space that can have complex parameter dependencies. We present the Differential Evolution MCMC (DEMCMC) algorithm for sampling from the posterior probability distribution for planet masses and orbital parameters. DEMCMC improves upon the random walk proposal distribution of the traditional MCMC by using an ensemble of Markov chains to adaptively improve the proposal distribution. DEMCMC can sample more efficiently from high-dimensional parameter spaces that have strong correlations between model parameters. We provide an overview of the algorithm, along with results of algorithm tests for accuracy and performance. We present early results from the application to previously announced multi-planet systems.
Ford Eric B.
Nelson Benjamin
Payne Matthew J.
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