Reserch On Dimension Reduction In Bayesion Statistics Based On Sliced Inverse Regression

With the development of computer technology and the arrival of the era of large data,massive data is filling our learning,work and life in all aspects.In the face of the increasing number of high-dimensional data,how to extract useful information from a large number of data has become one of the important subjects that statisticians faced.Bayesian statistics is an important class of statistics.It is based on the overall information,sample information and priori information for statistical inference.The basic method of Bayesian inference is to combine the priori information about the unknown parameters with the sample information,then to obtain the posterior information according to Bayes' theorem,and then to infer the unknown parameters according to the posterior information.But in the complex high-dimensional problems,the characteristics of posterior distribution are not well defined.Monte Carlo algorithm(MCMC)is a commonly used statistical simulation algorithm,which is based on Bayesian statistical thinking of analog sampling calculation,and it can be well simulated for the Bayesian estimation.The adaptive MCMC algorithm is an improvement on the general MCMC algorithm.However,in the case of finite samples,there are many problems in adaptive MCMC simulation of high-dimensional data.The inaccuracy of estimation and the low efficiency of the algorithm are the most serious problems.At this time,the dimension reduction of the high-dimensional data will have a significant role.Sliced inverse regression is an important member of IR family.It is an important sufficient dimension reduction method by minimizing the quadratic objective function.The basic idea of the inverse regression is to replace the prediction space with the projection of the prediction vector on the subspace of the prediction space without loss of the information of the conditional distribution Y | X.In this paper,we study the basic theory and method of Bayesian statistics,MCMC algorithm and adaptive MCMC algorithm,and I propose a new adaptive MCMC algorithm based on dimensionality reduction of high dimensional space,combined with AM algorithm and sliced inverse regression method.Through the simulation experiment,the autocorrelation coefficient of the sample is used to study the convergence of the algorithm.