Bayesian estimation of correlation functions

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.

arXiv commentSee (v1) for the original Angel's version and the article's history background. Changes: different priors for zero frequency; Fig. 5 redrawn; Section VI renamed and extended; App. B extended by non-factorizable priors; Added Apps. D, E, F, G, and H, and 9 references; Style and format changes throughout. Many of these changes reflect a year of experience in applying the theory to real-world data

References in corpus (8)

• Quantum Computing in the NISQ era and beyond
• Understanding the Lomb-Scargle Periodogram
• Quantum algorithms for quantum chemistry and quantum materials science
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Investigating the limits of randomized benchmarking protocols
• Practical Bayesian Tomography
• Spatial Noise Correlations in a Si/SiGe Two-Qubit Device from Bell State Coherences
• Exact numerical simulation of power-law noises

Cited by in corpus (5)

• Noise-correlation spectrum for a pair of spin qubits in silicon
• Spatial noise correlations beyond nearest-neighbor in ${}^{28}$Si/SiGe spin qubits
• The origins of noise in the Zeeman splitting of spin qubits in natural-silicon devices
• Noise cross-correlations from single-shot measurements
• Spin-qubit readout analysis based on a hidden Markov model