论文标题
相关噪声II的有效建模。具有快速可扩展方法的灵活噪声模型
Efficient modeling of correlated noise II. A flexible noise model with fast and scalable methods
论文作者
论文摘要
相关的噪声会影响大多数天文数据集并忽略其核算可能导致虚假的信号检测，尤其是在低信号到噪声条件下，这通常是追求新发现的情况。例如，在具有径向速度时间序列的系外行星检测领域中，出色的可变性可以诱导错误检测。但是，经常使用白噪声近似，因为分析数据时相关噪声的考虑意味着更复杂的分析。此外，计算成本通常会缩放为数据集大小的立方体。 对于某些有限类的相关噪声模型，有一些特定的算法可用于降低计算成本。在高斯过程回归的背景下，这种速度的提高特别有用，但是，它以噪声模型的一般性为代价。 在这里，我们介绍了S+叶噪声模型，这使我们能够考虑到相对于数据集大小的计算成本的线性缩放的大量相关噪声。 S+叶模型尤其包括准碘核和校准噪声的混合物。通过稀疏表示噪声的协方差矩阵以及用于矩阵反转，求解，确定性计算等的专用算法的稀疏表示，使这种有效的建模成为可能。 我们应用了S+叶模型来重新分析HD 136352的HARPS径向速度时间序列。我们说明了S+叶模型在处理各种噪声源时的灵活性。我们证明了考虑相关噪声，尤其是校准噪声的重要性，以正确评估检测到的信号的重要性。 我们提供了S+叶模型的开源实现，可在https://gitlab.unige.ch/jean-baptiste.delisle/spleaf上获得。
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.
