基于混合先验分布的贝叶斯因子分析模型

Bayesian Model for Factor Analysis Using Mixing Prior Distribution

针对现有因子分析模型不能充分融合模型参数信息问题,通过研究因子分析模型的统计结构,构造了参数的混合先验分布;利用贝叶斯定理证明了模型因子载荷阵的条件后验分布为矩阵t分布,协方差阵的条件后验分布为逆Wishart分布.实证研究表明:由于参数先验分布的作用,贝叶斯因子分析结果与传统的因子分析之间存在明显的差异.

This paper uses the Bayesian method to study the parameters＇ estimation in the factor model to solve the problem that the current method cannot reveal the information about the parameters in the model. We have designed a mixing prior for the model＇s parameters according to the model＇s statistical structure, inference and their marginal posterior distribution. The conditional posterior distribution of factor loading matrix and the covariance matrix are matrix student distribution and invert Wishart distribution. The results show that, owing to the role of the parameters＇ prior, there is distinctive difference between the results acquired by the Bayesian factor analysis method and that by the traditional factor analysis method.