一种用于径向速度数据中系外行星拟合和发现的仿射不变采样器
An Affine-Invariant Sampler for Exoplanet Fitting and Discovery in Radial Velocity Data
摘要：
马尔可夫链蒙特卡罗（MCMC）被证明是强大的贝叶斯推断，特别是系外行星径向速度拟合，因为MCMC提供更多的统计信息，并使更好地利用数据比常见的方法，如卡方拟合。然而，在这些问题中遇到的非线性密度函数可以使MCMC耗时。本文将仿射不变性集合采样器应用于径向速度数据的轨道参数提取。这种新的采样器只有一个自由参数，它不需要太多的调整良好的性能，这是非常重要的自动化。该采样器的自相关时间对于所有参数都大致相同，并且远小于Metropolis-Hastings，这意味着它需要更少的函数调用来产生相同数量的独立样本。在相同的计算条件下，仿射不变采样器使MCMC算法的计算速度比Metropolis-Hastings算法提高了数百倍。这种新颖的采样器将是涉及大型数据集的项目的理想选择，例如行星分布的统计调查。集成采样器的最大障碍是存在多个局部最优，我们提出了一种聚类技术来处理局部最优聚类的基础上的可能性的步行者在合奏。我们证明了采样器对实际径向速度数据的有效性。
英文摘要：
Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like chi-square fitting. However, the non-linear density functions encountered in these problems can make MCMC time-consuming. In this paper, we apply an ensemble sampler respecting affine invariance to orbital parameter extraction from radial velocity data. This new sampler has only one free parameter, and it does not require much tuning for good performance, which is important for automatization. The autocorrelation time of this sampler is approximately the same for all parameters and far smaller than Metropolis-Hastings, which means it requires many fewer function calls to produce the same number of independent samples. The affine-invariant sampler speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the same computing situation. This novel sampler would be ideal for projects involving large datasets such as statistical investigations of planet distribution. The biggest obstacle to ensemble samplers is the existence of multiple local optima; we present a clustering technique to deal with local optima by clustering based on the likelihood of the walkers in the ensemble. We demonstrate the effectiveness of the sampler on real radial velocity data.
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