MCMC算法在多维混合数据参数识别中的应用  

Application of MCMC Algorithm in Parameter Identification of Multidimensional Mixed Data

作　　者：石凯 李杰[3] 刘洪江 Shi Kai;Li Jie;Liu Hongjiang(School of Mathematics and Physics,Leshan Normal University,Leshan Sichuan 614000,China;School of Tourism,Leshan Normal University,Leshan Sichuan 614000,China;School of Statistics,Southwest University of Finance and Economics,Chengdu 611130,China)

机构地区：[1]乐山师范学院数理学院,四川乐山614000 [2]乐山师范学院旅游学院,四川乐山614000 [3]西南财经大学统计学院,成都611130

出　　处：《统计与决策》2021年第13期24-27,共4页Statistics & Decision

基　　金：四川省教育厅人文社会科学基金资助项目(18SB0223);乐山师范学院校级学科建设重点科研项目(WZD016)。

摘　　要：混合数据参数识别问题的研究一直备受关注,由于混合类型和混合权重无法直接观测,因此其实质是含有隐变量的不完全数据或者缺失数据。处理此类数据的难点在于参数的估计和识别,尤其是多维取值空间,会面临待估参数多、似然函数复杂等情况。文章给出了多维高斯分布假设下MCMC算法具体实施流程,并通过一个计算机模拟的三类别二维混合数据进行了实证研究,结果显示:MCMC算法达到了高度精确的区分效果,参数的样本估计值接近模拟生成的真值,能够为混合数据参数估计问题提供有效解决途径。The research on parameter identification of mixed data has been paid much attention. Because mixed type and mixed weight cannot be directly observed, the essence of mixed data is incomplete data or missing data with hidden variables. The difficulty in processing such data is the estimation and identification of parameters, and especially in the multidimensional value space, which will face the situation of many parameters to be estimated and complex likelihood function. This paper presents the specific implementation process of MCMC algorithm under the assumption of multidimensional Gaussian distribution, and conducts an empirical study through a computer simulation of three categories of 2 D mixed data. The results show that the MCMC algorithm achieves highly accurate distinction effect, and that the sample estimate of parameters is close to the true value generated by simulation, which can provide an effective solution to the problem of parameter estimation of mixed data.

关 键 词：MCMC算法 多维混合数据 贝叶斯统计 GIBBS抽样 

分 类 号：TP274.2[自动化与计算机技术—检测技术与自动化装置]