Estimating red noise in quasi-periodic signals with MCMC-based Bayesian

Abstract

Multi-parameter Bayesian inferences based on Markov chain Monte Carlo (MCMC) samples have been widely used to estimate red noise in solar period-periodic signals. To MCMC, proper priors and sufficient iterations are prerequisites ensuring the accuracy of red noise estimation. We used MCMC-based Bayesian inferences to estimate 100 groups of red noise synthesized randomly for evaluating its accuracy. At the same time, the Brooks-Gelman algorithm was employed to precisely diagnose the convergence of the Markov chains generated by MCMC. The root-mean-square error of parameter inferences to the synthetic data is only 1.14. Furthermore, we applied the algorithm to analyze the oscillation modes in a sunspot and a flare. A 70 s period is detected in the sunspot umbra in addition to 3- and 5-minute periods, and a 40 s period is detected in the flare. The results prove that estimating red noise with MCMC-based Bayesian has more high accuracy in the case of proper priors and convergence. We also find that the number of iterations increases dramatically to achieve convergence as the number of parameters grows. Therefore, we strongly recommend that when estimating red noise with MCMC-based Bayesian, different initial values must be selected to ensure that the entire posterior distribution is covered.

arXiv comment7 pages, 5 figures

References in corpus (18)

• A simple test for periodic signals in red noise
• A Bayesian test for periodic signals in red noise
• High-resolution Observations of the Shock Wave Behavior for Sunspot Oscillations with the Interface Region Imaging Spectrograph
• A large-scale search for evidence of quasi-periodic pulsations in solar flares
• Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra
• Quasi-Periodic Pulsations in Solar Flares: new clues from the Fermi Gamma-Ray Burst Monitor
• Observational Evidences of Electron-driven Evaporation in two Solar Flares
• Oscillations in a sunspot with light bridges
• A Compact Source for Quasi-Periodic Pulsation in an M-class Solar Flare
• Quasi-periodic Fast Propagating Magnetoacoustic Waves during the Magnetic Reconnection Between Solar Coronal Loops
• Multi-fluid approach to high-frequency waves in plasmas. III. Nonlinear regime and plasma heating
• Three-minute wave enhancement in the solar photosphere
• Significance testing for quasi-periodic pulsations in solar and stellar flares
• Quasi-periodic pulsations with periods that change depending on whether the pulsations have thermal or nonthermal components
• Stochastic transients as a source of quasi-periodic processes in the solar atmosphere
• Quasi-periodic pulsations with multiple periods in hard X-ray emission
• High-frequency Oscillations in the Atmosphere above a Sunspot Umbra
• Spatial Distributions of Sunspot Oscillation Modes at Different Temperatures

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