Robust Factor Analysis Model

Factor analysis model is the most commonly used technique to reduce the dimension of covariance matrix in multivariate statistical analysis.The existing analysis methods are mainly based on the normal assumption.When the observed data have heavy tails or outliers,the assumption of normality will make the estimation of parameters lose robustness.Instead of multivariate normal distribution,this paper adopts multivariate T distribution with unknown degree of freedom,and uses fully Bayesian method to analyze the factor analysis model.Since the full conditional posterior density of degrees of freedom contains an intractable terms,the traditional M-H algorithm needs to use numerical method to approximate the value of this item,which leads to inexact results and/or time-consuming sampling process.To solve this problem,this paper uses the exchange algorithm to sample from the full conditional posterior distribution of degrees of freedom.The simulation results show that the proposed algorithm has significant advantages over the traditional M-H algorithm.