INFERRING THE ECCENTRICITY DISTRIBUTION
- Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementation of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.
- OSTI ID:
- 21483632
- Journal Information:
- Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 725; ISSN ASJOAB; ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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