Improving the Efficiency of Markov Chain Monte Carlo for Analyzing the Orbits of Extrasolar Planets

Abstract

Precise radial velocity measurements have led to the discovery of ~170 extrasolar planetary systems. Understanding the uncertainties in the orbital solutions will become increasingly important as the discovery space for extrasolar planets shifts to planets with smaller masses and longer orbital periods. The method of Markov chain Monte Carlo (MCMC) provides a rigorous method for quantifying the uncertainties in orbital parameters in a Bayesian framework (Ford 2005a). The main practical challenge for the general application of MCMC is the need to construct Markov chains which quickly converge. The rate of convergence is very sensitive to the choice of the candidate transition probability distribution function (CTPDF). Here we explain one simple method for generating alternative CTPDFs which can significantly speed convergence by one to three orders of magnitude. We have numerically tested dozens of CTPDFs with simulated radial velocity data sets to identify those which perform well for different types of orbits and suggest a set of CTPDFs for general application. Additionally, we introduce other refinements to the MCMC algorithm for radial velocity planets, including an improved treatment of the uncertainties in the radial velocity observations, an algorithm for automatically choosing step sizes, an algorithm for automatically determining reasonable stopping times, and the use of importance sampling for including the dynamical evolution of multiple planet systems. Together, these improvements make it practical to apply MCMC to multiple planet systems. We demonstrate the improvements in efficiency by analyzing a variety of extrasolar planetary systems.

46 pages, 5 figures, 2 tables, ApJ in press

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• TOI-1696 and TOI-2136: Constraining the Masses of Two Mini-Neptunes with HPF
• The study on transiting systems HAT-P-13, HAT-P-16 and WASP-32 through combining ground-based and TESS photometry
• Aliasing in the Radial Velocities of YZ Ceti: An Ultra-Short Period for YZ Ceti c?
• Two transiting hot Jupiters from the WASP survey: WASP-150b and WASP-176b
• Doppler-beaming in the Kepler light curve of LHS 6343 A
• Analysis of the public HARPS/ESO spectroscopic archive -- Jupiter-like planets around HD 103891 and HD 105779
• HATS-59b,c: A Transiting Hot Jupiter and a Cold Massive Giant Planet Around a Sun-Like Star
• TOI-5375 B: A Very Low Mass Star at the Hydrogen-Burning Limit Orbiting an Early M-type Star
• NGTS-13b: A hot 4.8 Jupiter-mass planet transiting a subgiant star
• Discovery of an inflated hot Jupiter around a slightly evolved star TOI-1789
• Dynamical masses of M-dwarf binaries in young moving groups: II - Toward empirical mass-luminosity isochrones
• Revised Properties and Dynamical History for the HD 17156 System
• Discovery and characterization of a dense sub-Saturn TOI-6651b
• Detecting Extra-solar Planets with a Bayesian hybrid MCMC Kepler periodogram
• SEEDS direct imaging of the RV-detected companion to V450 Andromedae, and characterization of the system
• Bayesian Methods for Exoplanet Science
• Detection of eccentric close-binary supermassive black holes with incomplete interferometric data
• Migration and Evolution of giant ExoPlanets (MEEP) II: Super-Jupiters and Lithium-rich Host Stars
• Accurate and efficient photo-eccentric transit modeling
• Estimation of Planetary Photometric Emissions for Extremely Close-in Exoplanets
• TOI-1743 b, TOI-5799 b, TOI-5799 c and TOI-6223 b: TESS discovery and validation of four super-Earth to Neptune-sized planets around M dwarfs
• A Trio of Giant Planets Orbiting Evolved Star HD 184010
• Detecting planet pairs in mean motion resonances via astrometry method
• Forecasting the detectability of known radial velocity planets with the upcoming CHEOPS mission
• True Masses using RV data with Hipparcos and Gaia Astrometry
• Discovery of a Nearby Habitable Zone Super-Earth Candidate Amenable to Direct Imaging
• The architecture of the GJ876 planetary system. Masses and orbital coplanarity for planets b and c
• A Consistent Orbital Stability Analysis for the GJ 581 System
• Maps and Masses of Transiting Exoplanets: Towards New Insights into Atmospheric and Interior Properties of Planets
• The GAPS Programme at TNG LXVIII. Characterization of the outer substellar companion around HD 72659 with a multi-technique approach
• Observing transiting exoplanets with the MicroObservatory: 43 new transit light curves of the hot Jupiter HAT-P-32b
• Characterizing the WASP-4 system with TESS and radial velocity data: Constraints on the cause of the hot Jupiter's changing orbit and evidence of an outer planet
• Improving exoplanet mass characterisation with Bayesian model selection using the Learned Harmonic Mean Estimator
• TOI-3757 b: A low density gas giant orbiting a solar-metallicity M dwarf
• A 2+1+1 quadruple star system containing the most eccentric, low-mass, short-period, eclipsing binary known
• TOI-6884b: A low-mass brown dwarf transiting a slightly evolved star
• K2-99 revisited: a non-inflated warm Jupiter, and a temperate giant planet on a 522-d orbit around a subgiant