对数正态多层贝叶斯模型的参数估计

Parameter estimation of lognormal multilayer Bayesian model

为了更好地捕捉呈偏态分布数据的变化,提高统计推断的精确度,将对数正态多层先验分布的构造方法与贝叶斯定理结合建立了对数正态多层贝叶斯模型。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。

In order to better capture the changes of skewed distribution data and improve the accuracy of statistical inference,this paper combines the construction method of lognormal multilayer prior distribution with Bayesian theorem to establish a lognormal multilayer Bayesian model.The Gibbs sampling algorithm is used to estimate the unknown parameters,and the convergence of the iterative chain generated by the Gibbs algorithm is diagnosed.The random simulation results show that the Bayesian estimation is better than the maximum likelihood estimation under the relative error and MSE(mean square error)criteria.Finally,the empirical analysis proves that the established model is feasible.