标题： 亚赫兹频率下的精确谱估计：闭合形式后验和贝叶斯噪声投影 显示英文标题

标题： Precision spectral estimation at sub-Hz frequencies: closed-form posteriors and Bayesian noise projection

摘要： 我们提出了一种贝叶斯方法，用于估计多变量高斯时间序列中的谱量。该方法基于周期图和Wishart统计量，在任何给定频率下，为各个功率谱密度的边缘后验分布、成对相干性、多重相干性以及完整的交叉谱密度矩阵的联合后验分布提供了闭合形式的表达式。在噪声投影的背景下——其中某一序列被建模为其他序列的滤波版本的线性组合加上一个背景成分——该方法还为灵敏度（即滤波器传递函数）和背景的功率谱密度提供了闭合形式的后验分布。该方法最初是为分析欧洲空间局LISA路径探测器任务的数据而开发的，特别适用于非常低频的数据，在这种情况下，长时间的观测时间使得无法通过对大量周期图进行平均来处理，而这些周期图本来可以被视为近似正态分布。 显示英文摘要

摘要： We present a Bayesian method for estimating spectral quantities in multivariate Gaussian time series. The approach, based on periodograms and Wishart statistics, yields closed-form expressions at any given frequency for the marginal posterior distributions of the individual power spectral densities, the pairwise coherence, and the multiple coherence, as well as for the joint posterior distribution of the full cross-spectral density matrix. In the context of noise projection - where one series is modeled as a linear combination of filtered versions of the others, plus a background component - the method also provides closed-form posteriors for both the susceptibilities, i.e., the filter transfer functions, and the power spectral density of the background. Originally developed for the analysis of the data from the European Space Agency's LISA Pathfinder mission, the method is particularly well-suited to very-low-frequency data, where long observation times preclude averaging over large sets of periodograms, which would otherwise allow these to be treated as approximately normally distributed.