Bayes Statistical Diagnosis Of Generalized Nonlinear Models

Bayes statistical diagnosis of generalized nonlinear model is studied in this paper.Firstly,the parameter estimation of the generalized nonlinear model is carried out,and a Bayes estimation method is proposed to estimate the parameter values by extracting the observed values from the conditional posterior distribution of the parameters.The mixed algorithm combining the M-H algorithm and Gibbs sampling algorithm in the MCMC method is used for analysis to analyze the model.The parameters values are extracted through the conditional posterior distribution of the parameters at each iteration,and the convergence of the Markov chain at iteration is verified by using the sample path figure and the mean traverse figure of the parameters.The Bayes estimation of parameter is obtained by calculating the posterior mean value of the Markov chain after the chain achieve convergence.Secondly,the statistical diagnosis of the model data is carried out from two aspects: case-deletion model and Bayes local influence analysis.Based on the case-deletion model and using the posterior mean values of the parameters which are obtained by the MCMC method,we then propose the diagnostic tools such as the Cook posterior mean distance and the difference of deviance to determine outfielders and/or influential cases in the data.Then use the Bayes local influence analysis method to evaluate the effect of minor perturbations to the prior distribution,sample distribution,and of the sample data,with the Bayes factor or Cook posterior mean distance as the objective function,first-order local influence measures,first-order adjustment local influence measures or second-order local influence measures,second-order adjustment local influence measures are established to analyze the local influence of the model and identify strong influential cases in the data.Finally,through empirical analysis,the Bayes parameter estimation and identification of the outfielders or influential cases are carried out in the data,so as to verify the effectiveness and feasibility of Bayes statistical diagnosis method in the generalized nonlinear model.