Application Of Bayesian Statistical Methods Based On MCMC In The Hierarchical Normal Model

The research of social science tends to involve hierarchical data,and the objects of research generally have different nested structures and hierarchies.At this point,if the traditional classical regression model is chosen,biased parameter estimation and inaccurate statistical inference can be obtained,and the ideal method is to establish a hierarchical model.The hierarchical normal model is a kind of hierarchical model.In the process of studying the metabolism data of the male and female,the observation data has obvious characteristics of layered,so combining with the characteristics of data distribution this paper proposed hierarchical normal model to analyze the actual case study,achieving good results.Bayesian probability is one of the two major statistical probability,its inference theory and analysis method can be almost used as a research tool in various fields.In this paper,some important conclusions of the hierarchical normal model are derived by Bayesian method.In view of the complexity of hierarchical model parameters,this paper uses MCMC method to estimate the unknown parameters in the model.In the process of solving the model,Bayes method is used to determine the conditional posterior probability distribution of the unknown parameters,and the Gibbs sampling algorithm is employed to estimate the parameters,and the convergence of the Markov chain generated by MCMC method is determined.In the convergence diagnosis,this paper mainly combines the methods of image discrimination,ergodic mean and variance ratio method to determine,and uses the idea and principle of variance ratio method to obtain the potential scale reduction factor value of each unknown parameter in the model.Finally,the reliability of each parameter estimation based on Gibbs sampling algorithm is verified by comprehensive analysis of convergence criteria and image.