INFERRING THE ECCENTRICITY DISTRIBUTION
INFERRING THE ECCENTRICITY DISTRIBUTION
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DOI：
10.1088/0004-637x/725/2/2166
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发表时间：
2010-08
期刊：
影响因子：
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通讯作者：
D. Hogg;A. Myers;J. Bovy
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文献类型：
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作者：
D. Hogg;A. Myers;J. Bovy
双星和系外行星偏心率的标准最大似然估计器偏差很大，因为估计的偏心率往往大于真实的偏心率。与大多数重要的可观察量一样，估计偏心率的简单直方图并不能很好地估计真实的偏心率分布。在这里，我们开发并测试了一种分层概率方法来执行相关的荟萃分析，即推断真实的偏心率分布，将单个恒星偏心率的似然函数或偏心率的后验概率分布的采样（在给定的、无信息的先验条件下）作为输入。该方法是分层贝叶斯模型的简单实现；它也可以被视为一种异方差反卷积。它可以应用于以有限精度测量的任何量——其他轨道参数，或者实际上任何类型的任何天文测量，包括星等、距离或光度红移——只要测量值已作为似然函数或后验采样进行传达。
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.