贝叶斯-MCMC方法求解Fisher方程参数识别问题

发布时间：2018-02-26 11:39

  本文关键词： Fisher方程 参数识别 采样算法　出处：《黑龙江大学自然科学学报》2017年01期 　论文类型：期刊论文

【摘要】：马尔科夫链蒙特卡洛方法(MCMC)是一种启发式的全局寻优算法。在贝叶斯框架下,给出利用MCMC方法求解Fisher方程参数识别反问题的一种新方法。该方法把参数识别反问题视为贝叶斯估计问题,利用基于自适应Metropolis算法和延迟拒绝算法的一种有效的自适应MCMC方法,得到大量来自后验概率的样本,不仅能够获得每个未知参数的估计值,还可以获得与之相关的各种不确定信息。数值试验结果表明,该方法具有精度高、收敛速度快且易于计算机实现等优点。
[Abstract]:Markov chain Monte Carlo method (MCMC) is a heuristic global optimization algorithm. A new method for solving the inverse problem of parameter identification of Fisher equation using MCMC method is presented. The inverse problem of parameter identification is regarded as Bayesian estimation problem, and an effective adaptive MCMC method based on adaptive Metropolis algorithm and delay rejection algorithm is used. A large number of samples from a posteriori probability can be obtained not only from the estimated values of each unknown parameter, but also from a variety of uncertain information related to it. The numerical results show that the method has a high accuracy. The convergent speed is fast and easy to be realized by computer.
【作者单位】： 大连海事大学数学系;
【基金】：国家自然科学基金资助项目(41304092)
【分类号】：O241.8
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本文编号：1537883