Bayesian Statistical Inference For Mode Regression Model With Nonignorable Missing Skew-normal Data

According to the skew characteristics of the real data in many disciplines,this thesis considers that the random error of the regression model follows a skewnormal distribution,which can effectively overcome the potential weakness of the normal assumption and capture the data skewness.With mode as the sign value of"most likely" of the population,mode modeling has been shown to accurately describe the relationship between the conditional mode of the response variable and the covariate.In addition,with the development of high-throughput technology,real data often exhibit characteristics such as missing and high-dimension.The Bayesian approach fully utilizes prior information and is widely applied in handling these challenging problems.However,in the framework of high-dimensional data analysis,relying simply on the Bayesian approach does not have computational advantages.The variational Bayesian approach reformulates the calculation of posterior conditional density as an optimization problem,providing a fast and deterministic Bayesian alternative.The main research work carried out in this thesis is as follows:First,the Bayesian estimation procedure of the mode regression model with nonignorable missing skew-normal data is studied by the MCMC sampling method.At first,when the response variable has nonignorable missing,the missingness mechanisms are defined by the Logistic regression model,and the Bayesian hierarchical model is constructed.Secondly,the hybrid sampling algorithm combining the Gibbs sampling and the M-H algorithm is constructed for sampling from the posterior distribution,and the Bayesian estimation of the unknown parameters is calculated.Finally,the simulation studies compare the results of different missing data mechanisms and diverse prior settings.The results show that diverse prior settings have the same conclusion and can not be ignored that the nonignorable missing mechanism model is superior to the random missing mechanism model in processing missing data.The analysis of electronic component damage data shows the feasibility of the approach used in this thesis.Second,a hybrid sampling algorithm with a skinny Gibbs sampler and an Schrodinger-Follmer sampler is used to study the variable selection and parameter estimation of a high-dimensional mode regression model with nonignorable skew-normal data.First of all,spike and slab priors are used to process highdimensional data,avoiding large matrix calculations.In addition,the missingness mechanism is defined by the Logistic regression model,and the high-dimensional Bayesian hierarchical model is derived according to the prior setting.Secondly,the“skinny Gibbs”sampling approach obtains the expression of the required posterior condition distribution based on the joint posterior of the complete data set.The SFS algorithm extracts samples from a non-closed posterior distribution.Finally,the simulation studies compare the results of different missing data mechanisms and diverse prior settings.The proposed approach is applied to Piedmont wine data,which shows practical applicability.Third,the Bayesian estimation procedure of the high-dimensional mode regression model with nonignorable missing skew-normal data is studied by the black-box variational Bayesian approach based on approximation.In the first place,K-L divergence is used to find the optimal variational approximate distribution of the target posterior distribution in the mean-field variational distribution family.The gradient of ELBO is rewritten as an expectation form about variational objectives.The gradient of ELBO is calculated by Monte Carlo samples from the optimal variational approximate distribution.Then,the variance of the gradient is reduced by the control variable method,the variational parameters are obtained by the stochastic optimization algorithm based on variational objectives.In calculation,the SFS algorithm is selected to deal with the sampling problem in non-standardized distribution.Finally,the simulation studies and a real data example show that the black-box variational Bayesian approach is effective in dealing with high-dimensional data.