相关变量随机数序列产生方法

发布时间：2018-07-14 09:29

【摘要】：当采用蒙特卡罗方法对很多问题进行研究时,有时需要对多维相关随机变量进行抽样.之前的研究表明:在协方差矩阵满足正定条件时,可以采用Cholesky分解方法产生多维相关随机变量.本文首先对产生多维相关随机变量的理论公式进行了推导,发现采用Cholesky分解并不是产生多维相关随机变量的唯一方法,其他的矩阵分解方法只要能满足协方差矩阵的分解条件,同样可以用来产生多维相关随机变量.同时给出了采用协方差矩阵、相对协方差矩阵和相关系数矩阵产生多维随机变量的公式,以方便以后使用.在此基础上,利用一个简单测试题和Jacobi矩阵分解方法对上述理论进行了验证.通过对大亚湾中微子能谱进行抽样分析,Jacobi矩阵分解和Cholesky矩阵分解结果一致.针对核工程中的不确定性分析常用的~(238)U辐射俘获截面协方差矩阵进行分解时,由于协方差矩阵的矩阵本征值有负值,导致很多矩阵分解方法无法使用,在引入置零修正以后发现,与Cholesky对角线置零修正相比,Jacobi负本征值置零修正的误差更小.
[Abstract]:When Monte Carlo method is used to study many problems, it is sometimes necessary to sample multi-dimensional correlated random variables. Previous studies have shown that the Cholesky decomposition method can be used to generate multidimensional correlated random variables when the covariance matrix satisfies the positive definite condition. In this paper, the theoretical formula for generating multidimensional correlated random variables is first derived. It is found that Cholesky decomposition is not the only method for generating multidimensional correlated random variables. Other matrix decomposition methods can only satisfy the decomposition conditions of covariance matrices. It can also be used to generate multidimensional correlated random variables. At the same time, a formula for generating multidimensional random variables by using covariance matrix, relative covariance matrix and correlation coefficient matrix is given, which is convenient for future use. On this basis, a simple test problem and Jacobi matrix decomposition method are used to verify the above theory. The results of Jacobi matrix decomposition and Cholesky matrix decomposition are consistent by sampling analysis of neutrino spectra in Daya Bay. When the covariance matrix of ~ (238) U radiation capture cross section is decomposed for uncertainty analysis in nuclear engineering, because of the negative eigenvalue of the matrix, many matrix decomposition methods can not be used. It is found that the error of Jacobi negative eigenvalue zeroing correction is smaller than that of Cholesky diagonal zero correction.
【作者单位】：华北电力大学核科学与工程学院;
【基金】：国家自然科学基金(批准号:11390383) 中央高校基本科研业务费(批准号:2015ZZD12)资助的课题~~
【分类号】：O242.2

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