An affine-invariant sampler for exoplanet fitting and discovery in radial velocity data

Fengji Hou, Jonathan Goodman, David W. Hogg, Jonathan Weare, Christian Schwab

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Markov chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like chi-square fitting. However, the nonlinear density functions encountered in these problems can make MCMC time-consuming. In this paper, we apply an ensemble sampler respecting affine invariance to orbital parameter extraction from radial velocity data. This new sampler has only one free parameter, and does not require much tuning for good performance, which is important for automatization. The autocorrelation time of this sampler is approximately the same for all parameters and far smaller than Metropolis-Hastings, which means it requires many fewer function calls to produce the same number of independent samples. The affine-invariant sampler speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the same computing situation. This novel sampler would be ideal for projects involving large data sets such as statistical investigations of planet distribution. The biggest obstacle to ensemble samplers is the existence of multiple local optima; we present a clustering technique to deal with local optima by clustering based on the likelihood of the walkers in the ensemble. We demonstrate the effectiveness of the sampler on real radial velocity data.

LanguageEnglish
Article number198
Pages1-10
Number of pages10
JournalAstrophysical Journal
Volume745
Issue number2
DOIs
Publication statusPublished - 1 Feb 2012
Externally publishedYes

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samplers
extrasolar planets
radial velocity
sampler
Markov chains
Markov chain
inference
autocorrelation
planets
invariance
planet
tuning
orbitals
parameter

Cite this

Hou, Fengji ; Goodman, Jonathan ; Hogg, David W. ; Weare, Jonathan ; Schwab, Christian. / An affine-invariant sampler for exoplanet fitting and discovery in radial velocity data. In: Astrophysical Journal. 2012 ; Vol. 745, No. 2. pp. 1-10.
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An affine-invariant sampler for exoplanet fitting and discovery in radial velocity data. / Hou, Fengji; Goodman, Jonathan; Hogg, David W.; Weare, Jonathan; Schwab, Christian.

In: Astrophysical Journal, Vol. 745, No. 2, 198, 01.02.2012, p. 1-10.

Research output: Contribution to journalArticleResearchpeer-review

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