The efficiency of geometric samplers for exoplanet transit timing variation models

Noah W. Tuchow, Eric B. Ford, Theodore Papamarkou, Alexey Lindo

Research output: Contribution to journalArticle

Abstract

Transit timing variations (TTVs) are a valuable tool to determine the masses and orbits of transiting planets in multiplanet systems. TTVs can be readily modelled given knowledge of the interacting planets' orbital configurations and planet-star mass ratios, but such models are highly non-linear 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, non-linearity, and potential multimodality 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 data sets 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 data sets. For data sets 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 data set. 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.

Original languageEnglish (US)
Pages (from-to)3772-3784
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Volume484
Issue number3
DOIs
StatePublished - Apr 11 2019

Fingerprint

samplers
extrasolar planets
transit
sampler
time measurement
Markov chains
Markov chain
planets
planet
sampling
mass ratios
nonlinearity
Monte Carlo method
orbits
stars
orbitals
estimates
configurations
parameter
distribution

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Tuchow, Noah W. ; Ford, Eric B. ; Papamarkou, Theodore ; Lindo, Alexey. / The efficiency of geometric samplers for exoplanet transit timing variation models. In: Monthly Notices of the Royal Astronomical Society. 2019 ; Vol. 484, No. 3. pp. 3772-3784.
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The efficiency of geometric samplers for exoplanet transit timing variation models. / Tuchow, Noah W.; Ford, Eric B.; Papamarkou, Theodore; Lindo, Alexey.

In: Monthly Notices of the Royal Astronomical Society, Vol. 484, No. 3, 11.04.2019, p. 3772-3784.

Research output: Contribution to journalArticle

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