The Application Of Bayesian Hierarchical Model In The Data With Dichotomous Predicted Variables

The basic principle of Bayesian method is to use the likelihood information about parameters provided by observation data,combined with the prior information of parameters,and finally get the posterior information of parameters.Hierarchical model means that the observation value under different groups depends on the corresponding parameters of each group and the parameters of each group will be determined by its hyper-parameters,as a result,the model will present a hierarchical structure.Bayesian method is naturally suitable for this kind of hierarchical structure,and with the continuous development of Bayesian statistics,as well as the development of various statistical software and related packages,Bayesian method has become an important way to study hierarchical model.In this paper,Bayesian hierarchical model is used to study the case where the dependent variables are binary variables.Firstly,the construction and estimation method of Bayesian hierarchical model are discussed.Based on the introduction of traditional logistic regression model and hierarchical logistic regression model with linear parameters,a Bayesian hierarchical model with dichotomous dependent variables is constructed for grouped data.The joint posterior distribution is obtained from the likelihood function and prior distribution of the parameters in the model,and then the conditional posterior distributions of each parameter are obtained.After that,Gibbs sampling and Metropolis-Hastings sampling are used to estimate each parameter.Secondly,the simulation test and case analysis of the Bayesian hierarchical model are carried out.In the simulation test,the simulation data with sample size of 1500 are generated,the difference of parameter estimation effect between the traditional logistic regression model and the Bayesian hierarchical model is compared,and the performance of the Bayesian hierarchical model is measured.The results show that the forecasting classification of the simulation data is relatively satisfactory.In the case analysis,the strategy of Texas Hold'em poker is regarded as the research object.According to the selected data set of Texas Hold'em poker,the players are divided into three types: tight type,semi-loose type and loose type.The "lose" and "win" of players in each game are regarded as dichotomous dependent variables.Through Boruta method,seven influencing factors of the winning and losing of Texas poker players are screened out.Under sampling method is used to select samples as the training set to establish the Bayesian hierarchical model.This paper analyzes the game styles and strategies of three different types of players in the Hold'em poker,then it takes all the sample data as the test set to verify the prediction effect of the model through the performance measurement indicators.Finally,this paper improves the Bayesian hierarchical model in the case of some extreme outliers.The analysis results of the improved model show that by adding a random factor to the original model,the model can be more suitable for the application of actual data.