Calculation of Lagrange Multipliers in the Construction of Maximum Entropy Distributions in High Stochastic Dimension
Calculation of Lagrange Multipliers in the Construction of Maximum Entropy Distributions in High Stochastic Dimension
复制标题
高随机维最大熵分布构造中拉格朗日乘子的计算
DOI：
10.1137/120901386
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Christian Soize
中科院分区：
文献类型：
--
作者：
A. Batou;Christian Soize
本文研究的是在可用信息约束下，利用最大熵原理构造高维随机向量的概率分布。本文提出了一种适应高随机维的新算法，用于识别为考虑MaxEnt原理中的约束而引入的拉格朗日乘子。该算法基于(1)适当凸泛函的最小化和(2)构造定义为伊藤随机微分方程不变测度的概率分布。该方法通过一个专门用于生成物理一致和频谱兼容的加速度图的应用程序进行了验证。
The research addressed here concerns the construction of the probability distribution of a random vector in high dimension using the maximum entropy (MaxEnt) principle under constraints defined by the available information. In this paper, a new algorithm, adapted to the high stochastic dimension, is proposed to identify the Lagrange multipliers introduced to take into account the constraints in the MaxEnt principle. This new algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Ito stochastic differential equation. The methodology is validated through an application devoted to the generation of accelerograms which are physically consistent and spectrum compatible.