Article

# Bayesian exoplanet tests of a new method for MCMC sampling in highly correlated model parameter spaces

Physics and Astronomy Department, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
(Impact Factor: 5.11). 12/2010; 410(1):94 - 110. DOI: 10.1111/j.1365-2966.2010.17428.x

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.

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• "Note that this problem is also very closely related to the problem of detecting exoplanet signals in radial velocity data, which has attracted a lot of research attention in recent years (e.g. Gregory, 2011; Hou et al., 2014; Feroz et al., 2011). "
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• "Some of the other challenges in time domain astronomy that I have no room to discuss include high-precision pulsar timing (Liu et al. 2011), astroseismology (Appourchaux 2011) and planet detection (Gregory 2011; Ford et al. 2011). "
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• "Independently of earlier work, Cumming (2004) explored the connections between conventional periodogram methods and the Bayesian approach (albeit hampered by an incorrect marginal likelihood calculation); Cumming and Dragomir (2010) later extended this work, reproducing the Kepler periodogram of LC00. Ford (2005) (2008) and Gregory (2005) applied classic posterior sampling techniques (Metropolis random walk (MRW) and parallel tempering Markov chain Monte Carlo (MCMC), respectively) to orbit modeling; Gregory's approach uses a control system to tune the proposal parameters in a pilot run, and he has recently augmented his algorithm to include parameter updates based on genetic algorithms (Gregory 2011). Balan & Lahav (2008) applied an early, approximate adaptive MRW algorithm to the problem. "
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