卢茨-凯尔克公园
The Lutz-Kelker Paradox
摘要：
Lutz-Kelker修正的目的是对恒星的弛豫和星等给出一个无偏的估计，但它明确地表明它不是。这个悖论的结果是从应用有关样本统计的论点来处理个别恒星，并涉及错误地使用频率分布的概率密度函数的方式被认为是贝叶斯先验。它表明，贝叶斯概率分布的真实视差给定所观察到的视差选定的恒星是独立的分布的其他恒星。因此，Lutz-Kelker校正不应该用于单个恒星。这一结果具有重要意义的RR天琴座规模和解释结果从盖亚和依巴谷。Lutz-Kelker校正对影响视差有限样本的Trumpler-Weaver偏差处理不佳。使用数值积分计算真实校正，并通过Monte Carlo方法确认。
英文摘要：
The Lutz-Kelker correction is intended to give an unbiased estimate for stellar parallaxes and magnitudes, but it is shown explicitly that it does not. This paradox results from the application of an argument about sample statistics to the treatment of individual stars, and involves the erroneous use of a frequency distribution in the manner of a probability density function considered as a Bayesian prior. It is shown that the Bayesian probability distribution for true parallax given the observed parallax of a selected star is independent of the distribution of other stars. Consequently the Lutz-Kelker correction should not be used for individual stars. This result has important implications for the RR Lyrae scale and for the interpretation of results from Gaia and Hipparcos. The Lutz-Kelker correction is a poor treatment of the Trumpler-Weaver bias which affects parallax limited samples. A true correction is calculated using numerical integration and confirmed by a Monte Carlo method.
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