鞍点近似在恒星光观测周期探测中的应用
An application of Saddlepoint Approximation for period detection of stellar light observations
摘要：
在分析恒星的光变曲线时，人们感兴趣的主要特征之一是潜在的周期性行为。相应的观测结果是一种复杂类型的时间序列，具有不等间隔的时间点，有时伴随着不同的准确度。用于分析这些类型的数据的主要工具依赖于周期图状函数，其构造有期望的特征，使得峰值指示潜在周期的存在。在本文中，我们探讨了一个特殊的周期图的不规则观察的时间序列数据，类似于Thieler等。（2013）。我们在适当的峰值处确定潜在的周期，更重要的是，确定可量化的不确定性。我们的方法很容易推广到非参数方法，包括加权高斯过程回归周期图。我们还将这种方法扩展到相关背景噪声。所提出的周期检测方法依赖于基于具有正态分布分量的二次型的测试。我们实现鞍点近似，作为一个更快，更准确的替代目前使用的基于模拟的方法。功率分析的测试方法报告连同应用程序使用光变曲线从狩猎爆发的年轻明星公民科学项目。
英文摘要：
One of the main features of interest in analysing the light curves of stars is the underlying periodic behaviour. The corresponding observations are a complex type of time series with unequally spaced time points and are sometimes accompanied by varying measures of accuracy. The main tools for analysing these type of data rely on the periodogram-like functions, constructed with a desired feature so that the peaks indicate the presence of a potential period. In this paper, we explore a particular periodogram for the irregularly observed time series data, similar to Thieler et. al. (2013). We identify the potential periods at the appropriate peaks and more importantly with a quantifiable uncertainty. Our approach is shown to easily generalise to non-parametric methods including a weighted Gaussian process regression periodogram. We also extend this approach to correlated background noise. The proposed method for period detection relies on a test based on quadratic forms with normally distributed components. We implement the saddlepoint approximation, as a faster and more accurate alternative to the simulation-based methods that are currently used. The power analysis of the testing methodology is reported together with applications using light curves from the Hunting Outbursting Young Stars citizen science project.
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