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.
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Acknowledgements
We would like to thank the anonymous referee for helpful comments. S. Feng is supported by the Joint Funds of the National Natural Science Foundation of China (U1931107), the Key Applied Basic Research Program of Yunnan Province (2018FA035), and the Open Research Program (KLSA202007) of Key Laboratory of Solar Activity of National Astronomical Observatory of China. Y. Yang is supported by NSFC (11763004). We thank the science teams of the GOES, SDO/AIA.
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Liang, B., Meng, Y., Feng, S. et al. Estimating red noise in quasi-periodic signals with MCMC-based Bayesian. Astrophys Space Sci 365, 40 (2020). https://doi.org/10.1007/s10509-020-3744-4
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DOI: https://doi.org/10.1007/s10509-020-3744-4