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针对非高斯α稳定分布的联合参数估计问题,基于贝叶斯推理和马尔可夫链蒙特卡罗(MCMC)方法,提出一种将自适应Metropolis(AM)采样与延迟拒绝(DR)算法相结合的参数估计新方法.在贝叶斯框架下,本方法将所有待估计参数均视为随机变量,把参数估计问题转化为概率计算问题;然后通过将全局自适应与局部自适应采样相结合,可以快速构造出接近目标分布的提议函数,从而有效地提高了MCMC方法的抽样效率.仿真结果表明,该方法能够更加快速、准确地估计出α稳定分布的4个特征参数,且具有更好的鲁棒性和灵活性.
Aiming at the joint parameter estimation problem of non-Gaussian α stable distribution, based on Bayesian inference and Markov chain Monte Carlo (MCMC) method, an adaptive Metropolis (AM) sampling is combined with delayed rejection (DR) In Bayesian framework, this method treats all the parameters to be estimated as random variables and transforms the parameter estimation problem into the probability calculation problem. Then by combining global adaptive and local adaptive sampling, Which can quickly construct the proposed function close to the target distribution and effectively improve the sampling efficiency of the MCMC method.The simulation results show that the proposed method can estimate the four characteristic parameters of α stable distribution more quickly and accurately and has better Robustness and flexibility.