Bayesian estimation of correlation functions

TL;DR

This paper introduces a Bayesian approach for estimating correlation functions, providing probabilistic distributions and uncertainty measures for auto- and cross-correlations in stationary processes, enhancing spectral analysis and noise modeling.

Contribution

It presents a non-parametric Bayesian method for estimating correlation functions and spectra, including a technique to generate correlated noise with specified spectral properties.

Findings

Provides probability distributions for correlation estimates

Enables assessment of certainty levels in correlation measurements

Offers a method to generate correlated noise with a given spectrum

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 non-parametric 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.