相关噪声II的有效建模。灵活的噪声模型，具有快速和可扩展的方法
Efficient modeling of correlated noise II. A flexible noise model with fast and scalable methods
摘要：
相关噪声会影响大多数天文数据集，忽略它可能会导致虚假信号检测，特别是在低信噪比条件下，这通常是追求新发现的背景。例如，在利用径向速度时间序列进行系外行星探测的领域中，恒星的变化可能会导致错误的探测。然而，通常使用白噪声近似，因为在分析数据时考虑相关噪声意味着更复杂的分析。此外，计算成本可能是令人望而却步的，因为它通常与数据集大小的立方成比例。对于某些受限类别的相关噪声模型，可以使用特定的算法来帮助降低计算成本。这种速度的提高在高斯过程回归的上下文中特别有用，然而，它是以牺牲噪声模型的通用性为代价的。在这里，我们提出了S+LEAF噪声模型，它允许我们考虑到一个大类的相关噪声与线性缩放的计算成本相对于数据集的大小。S+LEAF模型特别包括准周期核和校准噪声的混合。这种有效的建模是可能的噪声的协方差矩阵的稀疏表示和使用专用的算法矩阵求逆，求解，行列式计算等，我们应用S+叶模型重新分析的HARPS径向速度HD 136352时间序列。我们说明了S+LEAF模型在处理各种噪声源的灵活性。我们证明了考虑相关噪声的重要性，特别是校准噪声，以正确评估检测到的信号的意义。我们提供了S+LEAF模型的开源实现，可在https://gitlab.unige.ch/jean-baptiste.delisle/spleaf上获得。
英文摘要：
Correlated noise affects most astronomical datasets and to neglect accounting for it can lead to spurious signal detections, especially in low signal-to-noise conditions, which is often the context in which new discoveries are pursued. For instance, in the realm of exoplanet detection with radial velocity time series, stellar variability can induce false detections. However, a white noise approximation is often used because accounting for correlated noise when analyzing data implies a more complex analysis. Moreover, the computational cost can be prohibitive as it typically scales as the cube of the dataset size. For some restricted classes of correlated noise models, there are specific algorithms that can be used to help bring down the computational cost. This improvement in speed is particularly useful in the context of Gaussian process regression, however, it comes at the expense of the generality of the noise model. Here, we present the S+LEAF noise model, which allows us to account for a large class of correlated noises with a linear scaling of the computational cost with respect to the size of the dataset. The S+LEAF model includes, in particular, mixtures of quasiperiodic kernels and calibration noise. This efficient modeling is made possible by a sparse representation of the covariance matrix of the noise and the use of dedicated algorithms for matrix inversion, solving, determinant computation, etc. We applied the S+LEAF model to reanalyze the HARPS radial velocity time series of HD 136352. We illustrate the flexibility of the S+LEAF model in handling various sources of noise. We demonstrate the importance of taking correlated noise into account, and especially calibration noise, to correctly assess the significance of detected signals. We provide an open-source implementation of the S+LEAF model, available at https://gitlab.unige.ch/jean-baptiste.delisle/spleaf.
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