ε-代换类先验分布族的贝叶斯稳健性分析

Bayesian Robustness Analysis of Prior Distribution Family of ε-substitution Class

对ε-代换类:Γ={π:π=(1-ε)π0+εq,q∈D(0≤ε≤1)的贝叶斯稳健性进行分析,π0是选定的先验分布,D为分布集.首先讨论了分布集D的选择对后验稳健性的影响.其次讨论了当D的选择合理时,ML-Ⅱ估计■是后验稳健的,并以■为先验分布,分别对正态分布进行稳健贝叶斯分析.

To analyze the Bayesian robustness of e-substitution class： Γ={π：π=（1-ε）π0＋εq,q∈D} 0≤ε≤1,π0 is selected prior distribution, D is distribution set. Firstly, discusses the influence of distribution set D to posterior robustness. Secondly, to the point when the selection of D is reasonable, ML-II estimation π is posterior robust. Takes π to be prior distribution, does the Bayesian robustness analysis to the normal distribution respectively.