Inferring the Eccentricity Distribution
Abstract
Standard maximumlikelihood estimators for binarystar and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most nontrivial 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 metaanalysis, 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 2010
 DOI:
 10.1088/0004637X/725/2/2166
 arXiv:
 arXiv:1008.4146
 Bibcode:
 2010ApJ...725.2166H
 Keywords:

 binaries: general;
 methods: data analysis;
 methods: statistical;
 planetary systems;
 planets and satellites: fundamental parameters;
 stars: kinematics and dynamics;
 Astrophysics  Solar and Stellar Astrophysics;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 ApJ