行星轮系径向速度的综合分析
An Integrated Analysis of Radial Velocities in Planet Searches
摘要：
我们讨论了贝叶斯方法分析行星搜索的径向速度。我们使用精确和近似的分析和数值技术相结合，以有效地评估卡方的轨道参数的多个值，并进行边缘化积分为一个单一的行星，包括长期趋势的可能性。其结果是一个强大的算法，是足够快的实时分析中使用的输出约束的轨道参数和误报警概率的行星和长期趋势。参数和比值比的约束，我们得到比较以及与以前的计算基于马尔可夫链蒙特卡罗方法，我们比较我们的结果与其他技术估计虚警概率和错误的轨道参数。由于试验次数的不同，贝叶斯分析的虚警概率系统地高于频率论虚警概率。我们表明，上的速度振幅的上限圆轨道推导出的偏心率小于约0.5的偏心轨道的振幅的上限是一个很好的估计。
英文摘要：
We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate chi-squared for multiple values of orbital parameters, and to carry out the marginalization integrals for a single planet including the possibility of a long term trend. The result is a robust algorithm that is rapid enough for use in real time analysis that outputs constraints on orbital parameters and false alarm probabilities for the planet and long term trend. The constraints on parameters and odds ratio that we derive compare well with previous calculations based on Markov Chain Monte Carlo methods, and we compare our results with other techniques for estimating false alarm probabilities and errors in derived orbital parameters. False alarm probabilities from the Bayesian analysis are systematically higher than frequentist false alarm probabilities, due to the different accounting of the number of trials. We show that upper limits on the velocity amplitude derived for circular orbits are a good estimate of the upper limit on the amplitude of eccentric orbits for eccentricities less than about 0.5.
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