Abstract
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the certainty level of the estimation. Our results apply to general stationary processes and their essence is a nonparametric estimation of spectra. It allows one to better understand the statistical noise fluctuations, assess the correlations between two variables, and postulate parametric models of spectra that can be further tested. We also propose a method to numerically generate correlated noise with a given spectrum.
| Original language | English |
|---|---|
| Article number | 043166 |
| Journal | Physical Review Research |
| Volume | 4 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
ASJC Scopus subject areas
- General Physics and Astronomy