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Keywords:

  • methods: numerical;
  • methods: statistical;
  • techniques: radial velocities;
  • astrometry;
  • planetary systems

ABSTRACT

The Markov chain Monte Carlo (MCMC) method is a powerful technique for facilitating Bayesian non-linear model fitting. In many cases, the MCMC exploration of the parameter space is very inefficient, because the model parameters are highly correlated. Differential evolution MCMC is one technique that addresses this problem by employing multiple parallel chains. We present a new method that automatically achieves efficient MCMC sampling in highly correlated parameter spaces, which does not require additional chains to accomplish this. It was designed to work with an existing hybrid MCMC (HMCMC) algorithm, which incorporates parallel tempering, simulated annealing and genetic cross-over operations. These features, together with the new correlated parameter sampler, greatly facilitate the detection of a global minimum in χ2. The new HMCMC algorithm is very general in scope. Two tests of the algorithm are described employing (a) exoplanet precision radial velocity (RV) data and (b) simulated space astrometry data. The latter test explores the accuracy of parameter estimates obtained with the Bayesian HMCMC algorithm on the assumed astrometric noise.