论文标题
用基于MCMC的贝叶斯估算准周期信号中的红色噪声
Estimating red noise in quasi-periodic signals with MCMC-based Bayesian
论文作者
论文摘要
基于马尔可夫链蒙特卡洛（MCMC）样品的多参数贝叶斯推论已被广泛用于估计太阳周期 - 周期性信号中的红噪声。对于MCMC而言，适当的先验和足够的迭代是前提条件，可确保红色噪声估算的准确性。我们使用基于MCMC的贝叶斯推论来估计合成的100组红噪声，以评估其准确性。同时，采用了Brooks-Gelman算法来精确诊断MCMC产生的Markov链的收敛。参数推断对合成数据的根平方误差仅为1.14。此外，我们应用了该算法来分析黑子和耀斑中的振荡模式。除3分钟和5分钟的时间外，在黑子蒙布拉（Sunspot Umbra）中还检测到了70 s的周期，并且在耀斑中检测到40 s的周期。结果证明，在适当的先验和收敛的情况下，用基于MCMC的贝叶斯估算红色噪声具有更高的精度。我们还发现，随着参数数量的增长，迭代次数急剧增加以达到收敛。因此，我们强烈建议在用基于MCMC的贝叶斯估算红噪声时，必须选择不同的初始值以确保涵盖整个后验分布。
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.
