二维非线性抛物型方程参数反演的贝叶斯推理估计

The estimated Bayesian inference of two-dimensional nonlinear parabolic equation parameter inversion

为了克服观测数据有限以及数据存在一定误差对参数反演结果的影响,提出了一种参数反演的有效算法.根据已知参数的先验分布和已经获得的有误差的监测数据,以贝叶斯推理作为理论基础,获得参数的联合后验概率密度函数.再利用马尔科夫链蒙特卡罗模拟对后验分布进行采样,获得参数的后验边缘概率密度,由此得到了参数的数学期望等有效的统计量.数值模拟结果表明,此算法能够有效地解决二维非线性抛物型方程的参数识别反问题,且具有较高的精度.

In order to overcome the limited observation data with noise, an inversion of the effective pa- rameters algorithm is presented. First, according to the parameters,a priori distribution and the limited observation data with noise, Bayesian inference as a theoretical foundation, parameters of the joint poste- rior probability density function are obtained. Markov chain Monte Carlo simulation was taken to sample the posterior distribution to get the marginal posterior probability function of the parameters, and the statistical quantities such as the mathematic expectation were calculated. Experimental results show that this algorithm can successfully solve the problem of two-dimensional nonlinear parabolic equation param- eter inversion and inversion results have higher accuracy.