论文标题
在多波段时间序列数据中建模随机变异性
Modeling Stochastic Variability in Multi-Band Time Series Data
论文作者
论文摘要
为了为即将进行的大规模调查的时域天文学时代做准备，我们提出了多变量阻尼的随机步行过程的状态空间表示，作为一种工具，以分析具有异性效果测量误差的不规则间隔的多滤波器光曲线。我们采用计算高效且可扩展的Kalman过滤方法来评估似然函数，从而导致最大$ O（k^3n）$复杂性，其中$ k $是可用频段的数量，$ n $是$ k $频段的独特观察时间数量。与常用单变量高斯过程相比，这是一个重要的计算优势，该过程可以将所有多波段光曲线叠加在一个最大$ o（k^3n^3）$复杂性的一个向量中。使用如此有效的可能性计算，我们提供模型参数的最大似然估计和贝叶斯后验样品。提出了三个数字插图； （i）分析模拟的五波段光曲线，以与独立的单频拟合进行比较； （ii）分析从斯隆数字天空调查（SDSS）条带〜82获得的类星体的五波段光曲线，以估计短期可变性和时间表； （iii）分析重力镜头的$ g $ - 和$ r $ - 带灯曲线Q0957+561，以推断时间延迟。公开使用两个R包RDRW和TIMEDELAY，可公开使用建议的型号。
In preparation for the era of the time-domain astronomy with upcoming large-scale surveys, we propose a state-space representation of a multivariate damped random walk process as a tool to analyze irregularly-spaced multi-filter light curves with heteroscedastic measurement errors. We adopt a computationally efficient and scalable Kalman-filtering approach to evaluate the likelihood function, leading to maximum $O(k^3n)$ complexity, where $k$ is the number of available bands and $n$ is the number of unique observation times across the $k$ bands. This is a significant computational advantage over a commonly used univariate Gaussian process that can stack up all multi-band light curves in one vector with maximum $O(k^3n^3)$ complexity. Using such efficient likelihood computation, we provide both maximum likelihood estimates and Bayesian posterior samples of the model parameters. Three numerical illustrations are presented; (i) analyzing simulated five-band light curves for a comparison with independent single-band fits; (ii) analyzing five-band light curves of a quasar obtained from the Sloan Digital Sky Survey (SDSS) Stripe~82 to estimate the short-term variability and timescale; (iii) analyzing gravitationally lensed $g$- and $r$-band light curves of Q0957+561 to infer the time delay. Two R packages, Rdrw and timedelay, are publicly available to fit the proposed models.
