Research On Red Noise Estimation Method In Solar Observation Signal Based On HMC Algorithm

Solar quasi-periodic oscillation is the rhythmic modulation of electromagnetic radiation by the plasma in the solar atmosphere over a wide range of wavelengths.It is usually observed in the combined light curve of solar flares,sunspots and coronas,and can be observed from radio bands,visible light,extreme ultraviolet to x-rays.However,the oscillation mode in the light curve is usually suppressed by red noise,so it is difficult to characterize it.Therefore,how to detect a physically significant oscillating signal from red noise has become a long-term problem in astrophysics.For the red noise in astronomical signals,common representation methods such as the least square method and the Markov chain Monte Carlo(MCMC)method have some limitations.The least square method is only suitable for the characterization of simple models and through this method The root-mean-square error of the obtained results is large.The most commonly used algorithm in the MCMC method is the Metropolis-Hastings(MH)algorithm,which has a slow convergence rate.In addition,when the MCMC algorithm is actually used,most studies have not judged whether the Markov chain has converged,which may lead to erroneous results.Aiming at the problems of least square method and MCMC method,this paper adopts a new red noise estimation method-Hamilton Monte Carlo method(HMC)to realize the parameter estimation of red noise model.Compared with the least square method,this method can still effectively and accurately estimate the parameters of the model in the case of high dimensions.And overcome the shortcomings of the MH algorithm's slow convergence,reduce the random walk behavior of the MH algorithm,improve the effectiveness of the Markov chain,so that the algorithm can quickly converge.At the same time,for the problem of MCMC method's convergence test,this paper uses the German-Rubin method to test the posterior distribution of the MCMC method,that is,to judge the convergence of the Markov chain;and this method is used to corroborate the convergence rate ratio of the HMC algorithm.The fact that the MH algorithm is about ten times faster.Finally,the HMC method and chi-square test are applied to actual solar observation data such as sunspots and solar flares,and the quasi-periodic oscillation(QPP)in the solar activity is estimated by estimating the red noise in these observation signals.The effectiveness of the German-Rubin method in judging the convergence of the MCMC and the statistical aspects of the iterations required for convergence are confirmed,and the experimental results of multiple experiments prove that the red noise estimation method is compared with the current method.The HMC algorithm used is better.