对数正态多层贝叶斯混合模型的参数估计
Parameter Estimation of Lognormal Multilayer Bayesian Model
王志凯 1黄介武1
作者信息
- 1. 贵州民族大学数据科学与信息工程学院,贵阳 550025
- 折叠
摘要
用传统的正态多层贝叶斯混合模型在对具有均值异质性和方差异质性的偏态分布数据进行统计推断时效果不佳.针对这一问题,本文对数正态多层先验分布的构造与贝叶斯定理相结合,并引入到混合模型中,从而建立了对数正态多层贝叶斯混合模型.在混合模型的混合个数(k)已知的情况下,利用Gibbs抽样算法对各未知参数进行贝叶斯估计,并对使用Gibbs算法所生成的迭代链进行收敛性诊断.随机模拟结果显示,在相对误差、均方误差(MSE)准则下,贝叶斯估计的效果较似然估计更优.最后,通过实证分析证明了所建立的模型是切实可行的.
Abstract
In view of the fact that the traditional normal multi-layer Bayesian mixture model is not effective in the statistical inference of skewed distribution data with mean heterogeneity and variance heterogeneity,this paper combines the construction of log-normal multi-layer prior distribution with Bayesian theorem and introduces it into the mixture model,so as to establish a log-normal multi-layer Bayesian mixture model.In the case of known mixing number(k)of the mixture model,the Bayesian estimation of unknown parameters is performed by applying the Gibbs sampling algorithm,and the convergence of the iterative chain generated by the Gibbs algorithm is diagnosed.Random simulation results show that the effect of Bayesian estimation is better than that of likelihood estimation under the relative error and mean square error(MSE)criteria.Finally,the empirical analysis proves that the established model is feasible.
关键词
混合模型/正态多层贝叶斯混合模型/对数正态多层贝叶斯混合模型/贝叶斯估计/Gibbs算法Key words
hybrid model/normal multilayer bayesian mixture model/lognormal multilayer bayesian mixture model/bayesian estimation/gibbs algorithm引用本文复制引用
出版年
2024
NETL
NSTL
万方数据