基于贝叶斯理论的云模型参数估计研究  

Parameter Estimation of Cloud Model Based on Bayesian Theory

作　　者：高艳苹 吕王勇[1] 王玲玲[1] 蔡琳芝 Gao Yanping;Lv Wangyong;Wang Lingling;Cai Linzhi(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China)

机构地区：[1]四川师范大学数学与软件科学学院,成都610068

出　　处：《统计与决策》2019年第6期5-8,共4页Statistics & Decision

基　　金：国家自然科学基金青年项目(11601357);四川省科技厅应用基础研究项目(2017JY0159);四川省教育厅重点项目(2015ZA0030);可视化计算与虚拟现实四川省重点实验室项目(SCVCVR2018.08VS)

摘　　要：云模型共有三个未知参数:期望、熵、超熵。经典的云参数的估计方法有矩估计法和极大似然估计法,二者都是在将样本均值作为期望的估计值的前提下,分别求得熵和超熵的矩估计和极大似然估计。在期望不是一个未知参数,而是一个随机变量,且分布已知的假设下,应用贝叶斯理论,得到期望的后验分布及其后验估计,并基于期望的后验估计求得熵、超熵的后验矩估计和后验极大似然估计。以均方误差最小为准则,将经典的矩估计、极大似然估计与后验的矩估计、后验极大似然估计比较,得到后验的极大似然估计效果最优的结论。There are three unknown parameters in cloud model: expectation, entropy and hyper-entropy. Classical cloud parameter estimation methods include moment estimation and maximum likelihood estimation, both of which obtain the moment estimation and maximum likelihood estimation of entropy and hyper-entropy respectively on the premise of taking the sample mean as the expected value. Under the assumption that expectation is not an unknown parameter but a random variable with a known distribution, the paper uses Bayesian theory to obtain the expected posterior distribution, and relies the expected posterior estimation to obtain the posterior moment estimation and posterior maximum likelihood estimation of entropy and hyper-entropy. And then, taking the minimum mean square error as the criterion, the paper compares the classical moment estimation and maximum likelihood estimation with the posterior moment estimation and maximum likelihood estimation to acquire the optimal result of the posterior maximum likelihood estimation.

关 键 词：云模型 矩估计 极大似然估计 后验矩估计 后验极大似然估计 

分 类 号：O213[理学—概率论与数理统计]