论文标题
TD-Carma：带有灵活的Carma过程的无痛，准确且可扩展的估计值
TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes
论文作者
论文摘要
编码我们对宇宙扩展历史的理解的宇宙学参数可以通过重力镜头系统中的时间延迟的准确估计来限制。我们提出了TD-Carma，这是一种贝叶斯方法，可以通过对观察到的和不规则采样的光曲线进行建模作为连续自动回归移动平均值（CARMA）过程的实现来估计宇宙时间延迟。我们的模型说明了异质测量误差和微透镜，这是源亮度中独立外部长期可变性的附加来源。 CARMA协方差矩阵的半分离结构允许使用高斯过程建模进行快速，可扩展的可能性计算。我们使用嵌套采样方法从模型参数的关节后部分布中获得样本。这允许``无痛''贝叶斯计算，以直接的方式处理后验分布的预期多模式，而不需要规范起始值或时间延迟的初始猜测，与现有方法不同。此外，提出的采样程序会自动评估贝叶斯证据，从而使我们能够执行原则上的贝叶斯模型选择。 TD-Carma是简单的，通常不包括十几个未知参数。 We apply TD-CARMA to six doubly lensed quasars HS 2209+1914, SDSS J1001+5027, SDSS J1206+4332, SDSS J1515+1511, SDSS J1455+1447, SDSS J1349+1227, estimating their time delays as $-21.96 \pm 1.448$, $ 120.93 \ pm 1.015 $，$ 111.51 \ pm 1.452 $，$ 210.80 \ pm 2.18 $，$ 45.36 \ pm 1.93 $和$ 432.05 \ pm 1.950 $。这些估计与相关文献中得出的估计相一致，但通常更精确。
Cosmological parameters encoding our understanding of the expansion history of the Universe can be constrained by the accurate estimation of time delays arising in gravitationally lensed systems. We propose TD-CARMA, a Bayesian method to estimate cosmological time delays by modelling the observed and irregularly sampled light curves as realizations of a Continuous Auto-Regressive Moving Average (CARMA) process. Our model accounts for heteroskedastic measurement errors and microlensing, an additional source of independent extrinsic long-term variability in the source brightness. The semi-separable structure of the CARMA covariance matrix allows for fast and scalable likelihood computation using Gaussian Process modeling. We obtain a sample from the joint posterior distribution of the model parameters using a nested sampling approach. This allows for ``painless'' Bayesian Computation, dealing with the expected multi-modality of the posterior distribution in a straightforward manner and not requiring the specification of starting values or an initial guess for the time delay, unlike existing methods. In addition, the proposed sampling procedure automatically evaluates the Bayesian evidence, allowing us to perform principled Bayesian model selection. TD-CARMA is parsimonious, and typically includes no more than a dozen unknown parameters. We apply TD-CARMA to six doubly lensed quasars HS 2209+1914, SDSS J1001+5027, SDSS J1206+4332, SDSS J1515+1511, SDSS J1455+1447, SDSS J1349+1227, estimating their time delays as $-21.96 \pm 1.448$, $120.93 \pm 1.015$, $111.51 \pm 1.452$, $210.80 \pm 2.18$, $45.36 \pm 1.93$ and $432.05 \pm 1.950$ respectively. These estimates are consistent with those derived in the relevant literature, but are typically two to four times more precise.
