Maximum Entropy Spectral Analysis: an application to gravitational waves data analysis

研究问题: 如何利用最大熵与自回归表示估计时间序列的功率谱，并在较短的引力波数据中处理噪声谱不确定性对参数推断的影响？
方法与思路: 作者提供 Burg 递归算法的 Python 实现，比较递归停止准则和 Welch 谱估计，再联合处理噪声谱与 GW150914 系统参数推断。
材料陈述的贡献: 摘要称，在所用合成数据比较中 Burg 方法的谱估计偏差和方差更低，尤其适合较短序列，并展示噪声谱边际化的应用。
阅读关注点: 应核对自回归阶数与停止准则、合成谱和 Welch 比较设置，以及噪声谱边际化如何影响系统参数后验与不确定性表达。
阅读边界: 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未提供完整比较条件和数值结果，引力波案例的优势不能直接推广至经济序列。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

The Maximum Entropy Spectral Analysis (MESA) method, developed by Burg, offers a powerful tool for spectral estimation of a time-series. It relies on Jaynes' maximum entropy principle, allowing the spectrum of a stochastic process to be inferred using the coefficients of an autoregressive process AR( $p$ ) of order $p$ . A closed-form recursive solution provides estimates for both the autoregressive coefficients and the order $p$ of the process. We provide a ready-to-use implementation of this algorithm in a Python package called \texttt{memspectrum}, characterized through power spectral density (PSD) analysis on synthetic data with known PSD and comparisons of different criteria for stopping the recursion. Additionally, we compare the performance of our implementation with the ubiquitous Welch algorithm, using synthetic data generated from the GW150914 strain spectrum released by the LIGO-Virgo-Kagra collaboration. Our findings indicate that Burg's method provides PSD estimates with systematically lower variance and bias. This is particularly manifest in the case of a small (O( $5000$ )) number of data points, making Burg's method most suitable to work in this regime. Since this is close to the typical length of analysed gravitational waves data, improving the estimate of the PSD in this regime leads to more reliable posterior profiles for the system under study. We conclude our investigation by utilising MESA, and its particularly easy parametrisation where the only free parameter is the order $p$ of the AR process, to marginalise over the interferometers noise PSD in conjunction with inferring the parameters of GW150914.The Maximum Entropy Spectral Analysis (MESA) method, developed by Burg, offers a powerful tool for spectral estimation of a time-series. It relies on Jaynes' maximum entropy principle, allowing the spectrum of a stochastic process to be inferred using the coefficients of an autoregressive process AR($p$) of order $p$. A closed-form recursive solution provides estimates for both the autoregressive coefficients and the order $p$ of the process. We provide a ready-to-use implementation of this algorithm in a Python package called \texttt{memspectrum}, characterized through power spectral density (PSD) analysis on synthetic data with known PSD and comparisons of different criteria for stopping the recursion. Additionally, we compare the performance of our implementation with the ubiquitous Welch algorithm, using synthetic data generated from the GW150914 strain spectrum released by the LIGO-Virgo-Kagra collaboration. Our findings indicate that Burg's method provides PSD estimates with systematically lower variance and bias. This is particularly manifest in the case of a small (O($5000$)) number of data points, making Burg's method most suitable to work in this regime. Since this is close to the typical length of analysed gravitational waves data, improving the estimate of the PSD in this regime leads to more reliable posterior profiles for the system under study. We conclude our investigation by utilising MESA, and its particularly easy parametrisation where the only free parameter is the order $p$ of the AR process, to marginalise over the interferometers noise PSD in conjunction with inferring the parameters of GW150914.

摘要来源：arXiv

笔记与分组

分类依据与纠错

Maximum Entropy Spectral Analysis: an application to gravitational waves data analysis

作者的期刊发表依据

代码、数据与补充材料

最大熵谱分析及其在引力波数据分析中的应用

原文摘要

同方向的基础文献

同方向的基础文献