通过多输出高斯过程对天文多波段时间序列数据中的依赖结构进行建模
Modeling Dependence Structures in Astronomical Multi-Band Time Series Data via Multi-Output Gaussian Processes
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中文总结 AI 辅助
研究利用多输出高斯过程对天文多波段时间序列数据的依赖结构建模，提出基于协方差和潜在过程的互补公式，开发相关模型并应用于实际，为依科学目标选择依赖结构提供原则基础。
中文摘要 AI 辅助
现代天文时域调查经常收集多波段光变曲线，高斯过程为建模不规则采样和有噪声的时间序列数据提供了灵活的概率框架。以往对单个时间序列协方差核关注较多，对多波段依赖关系统计表示关注较少。本文提出用多输出高斯过程建模依赖结构的统一统计框架，包括基于协方差和潜在过程两种互补公式。通过开发相关模型并应用于多波段活动星系核变率和连续统回响映射，说明这些公式的实际意义，为依科学目标选择依赖结构提供原则基础。
英文摘要
Modern astronomical time-domain surveys routinely collect multi-band light curves that provide complementary information about the physical processes governing source variability. Gaussian processes (GPs) provide a flexible probabilistic framework for modeling irregularly sampled and noisy time-series data. While considerable attention has been devoted to developing covariance kernels for individual time series, comparatively less attention has been paid to the statistical representation of dependence among multiple photometric bands. In this work, we present a unified statistical framework for modeling such dependence structures using multi-output GPs. Within this framework, we consider two complementary formulations. The covariance-based formulation specifies dependence directly through matrix-valued covariance functions and emphasizes the stochastic properties of the observed light curves, including covariance functions and power spectral densities. In contrast, the latent-process formulation represents the observed light curves as transformations of latent GPs and emphasizes the physical mechanisms generating the observed dependence. To illustrate these formulations, we develop covariance-based and latent-process multi-output damped random walk models and derive their corresponding spectral representations. We further demonstrate the practical implications of dependence-structure modeling through applications to multi-band active galactic nucleus variability and continuum reverberation mapping. Rather than advocating a universally preferred formulation, this work provides a principled basis for selecting dependence structures according to the scientific objectives and clarifies how this choice influences the statistical characterization and scientific interpretation of stochastic variability in astronomical sources.
