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2010

Inferring the eccentricity distribution

Hogg, David W., Myers, Adam D., Bovy, Jo

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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.

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Murray, I., & Adams, R. P., 2010b, arXiv:1006.0868
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Gregory, P. C., 2005, ApJ, 631, 1198
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Zakamska, N. L., Pan, M., & Ford, E. B., 2010, MNRAS, in press (arXiv:1008.4152)
Original
2010
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