Efficient modeling of correlated noise

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. In this article, 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 the recently published planetary system 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.