Calibration Concordance for Astronomical Instruments via Multiplicative Shrinkage

Calibration data are often obtained by observing several well-understood objects simultaneously with multiple instruments, such as satellites for measuring astronomical sources. Analyzing such data and obtaining proper concordance among the instruments is challenging when the physical source models are not well understood, when there are uncertainties in “known” physical quantities, or when data quality varies in ways that cannot be fully quantified. Furthermore, the number of model parameters increases with both the number of instruments and the number of sources. Thus, concordance of the instruments requires careful modeling of the mean signals, the intrinsic source differences, and measurement errors. In this article, we propose a log-Normal model and a more general log-<i>t</i> model that respect the multiplicative nature of the mean signals via a half-variance adjustment, yet permit imperfections in the mean modeling to be absorbed by residual variances. We present analytical solutions in the form of power shrinkage in special cases and develop reliable Markov chain Monte Carlo algorithms for general cases, both of which are available in the Python module <i>CalConcordance</i>. We apply our method to several datasets including a combination of observations of <i>active galactic nuclei</i> (AGN) and spectral line emission from the <i>supernova remnant</i> E0102, obtained with a variety of X-ray telescopes such as <i>Chandra</i>, XMM- <i>Newton</i>, <i>Suzaku</i>, and <i>Swift</i>. The data are compiled by the <i>International Astronomical Consortium for High Energy Calibration</i>. We demonstrate that our method provides helpful and practical guidance for astrophysicists when adjusting for disagreements among instruments. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

校准数据通常通过多台仪器同时观测若干可充分表征的天体获取，例如用于测量天文源的卫星。当天体源物理模型尚未明确、“已知”物理量存在不确定度，或数据质量存在无法完全量化的变化时，分析此类数据并实现仪器间的合理一致性校准极具挑战。此外，模型参数数量随仪器总数与天体源总数的增加而增长。因此，实现仪器间的一致性校准，需要对平均信号、天体本征差异与测量误差进行精细化建模。本文提出了对数正态模型（log-Normal model）与更具普适性的对数t模型（log-t model），二者通过半方差校正契合平均信号的乘性特性，同时允许平均建模的偏差由残差方差吸收。我们针对特殊场景推导了幂收缩形式的解析解，并针对一般场景开发了可靠的马尔可夫链蒙特卡洛（Markov chain Monte Carlo）算法，二者均已封装至Python模块CalConcordance中。我们将所提方法应用于多组数据集，其中包括利用钱德拉（Chandra）、XMM-牛顿（XMM-Newton）、朱雀（Suzaku）与雨燕（Swift）等多款X射线望远镜获取的活动星系核（AGN）观测数据，以及超新星遗迹E0102的谱线辐射数据的组合数据集。该数据集由国际高能校准天文联盟（International Astronomical Consortium for High Energy Calibration）汇编而成。我们验证了所提方法可为天体物理学家调整仪器间的不一致性提供切实可行的指导。本文的补充材料（包含可用于复现研究工作的标准化材料说明）可通过在线补充资源获取。