Inferring the Eccentricity Distribution

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...

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Bibliographic Details
Published in:The Astrophysical journal 2010-12, Vol.725 (2), p.2166-2175
Main Authors: Hogg, David W, Myers, Adam D, Bovy, Jo
Format: Article
Language:English
Subjects:
Astronomy
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
BINARY STARS
CALCULATION METHODS
DATA ANALYSIS
Earth, ocean, space
Exact sciences and technology
FUNCTIONS
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL SOLUTIONS
MAXIMUM-LIKELIHOOD FIT
NUMERICAL SOLUTION
PROBABILISTIC ESTIMATION
PROBABILITY
RED SHIFT
STARS
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Summary: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.
ISSN:0004-637X
1538-4357
DOI:10.1088/0004-637X/725/2/2166