The efficiency of geometric samplers for exoplanet transit timing variation models

Tuchow, N. W., Ford, E. B., Papamarkou, T. and Lindo, A. (2019) The efficiency of geometric samplers for exoplanet transit timing variation models. Monthly Notices of the Royal Astronomical Society, 484(3), pp. 3772-3784. (doi: 10.1093/mnras/stz247)

Abstract

Transit timing variations (TTVs) are a valuable tool to determine the masses and orbits of transiting planets in multi-planet systems. TTVs can be readily modeled given knowledge of the interacting planets’ orbital configurations and planet-star mass ratios, but such models are highly nonlinear and difficult to invert. Markov chain Monte Carlo (MCMC) methods are often used to explore the posterior distribution for model parameters, but, due to the high correlations between parameters, nonlinearity, and potential multi-modality in the posterior, many samplers perform very inefficiently. Therefore, we assess the performance of several MCMC samplers that use varying degrees of geometric information about the target distribution. We generate synthetic datasets from multiple models, including the TTVFaster model and a simple sinusoidal model, and test the efficiencies of various MCMC samplers. We find that sampling efficiency can be greatly improved for all models by sampling from a parameter space transformed using an estimate of the covariance and means of the target distribution. No one sampler performs the best for all datasets. For datasets with near Gaussian posteriors, the Hamiltonian Monte Carlo sampler obtains the highest efficiencies when the step size and number of steps are properly tuned. Two samplers — Differential Evolution Monte Carlo and Geometric adaptive Monte Carlo, have consistently efficient performance for each dataset. Based on differences in effective sample sizes per time, we show that the right choice of sampler can improve sampling efficiencies by several orders of magnitude.

• Item Type: Articles
• Additional Information: EBF and NWT acknowledge the support of the Institute for CyberScience and the Center for Exoplanets and Habitable Worlds, which is supported by The Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. EBF and NWT were supported from NSF grant AST1616086, and NWT acknowledges support from the Penn State Center for Astrostatistics.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lindo, Dr Alexey and Papamarkou, Dr Theodore
• Authors: Tuchow, N. W., Ford, E. B., Papamarkou, T., and Lindo, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Monthly Notices of the Royal Astronomical Society
• Publisher: Oxford University Press
• ISSN: 0035-8711
• ISSN (Online): 1365-2966
• Published Online: 24 January 2019
• Copyright Holders: Copyright © 2019 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
• First Published: First published in Monthly Notices of the Royal Astronomical Society 484(3):3772-3784
• Publisher Policy: Reproduced in accordance with the publisher copyright policy