Modeling Dependence Structures in Astronomical Multi-Band Time Series Data via Multi-Output Gaussian Processes

2026-07-23

AI Summary

This work addresses the inadequate modeling of inter-band dependencies in astronomical multi-band time-series data by proposing two complementary multi-output Gaussian process paradigms: one explicitly captures statistical dependencies across bands through a matrix-valued covariance function, while the other reveals their underlying physical generation mechanisms via shared latent processes. The framework unifies established astrophysical priors—such as the damped random walk model and continuum reverberation mapping—and integrates power spectral density analysis to clarify the distinctions between different dependency structures in terms of both statistical representation and physical interpretability. Experiments on multi-band light curves of active galactic nuclei demonstrate that explicitly modeling inter-band dependencies significantly enhances both the accuracy of temporal modeling and scientific interpretability, thereby providing a principled basis for model selection aligned with scientific objectives.

Abstract

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.

Problem

• multi-band time series
• dependence structure
• Gaussian processes
• astronomical variability
• multi-output modeling

Innovation

• multi-output Gaussian processes
• dependence structure
• matrix-valued covariance
• latent processes
• damped random walk