The Analysis And Application Of High-Dimensional Data Based On Bayesian Statistics

With the development of modern science and technology,more and more high-dimensional data arises in diverse subject areas like biomedical science,genetic engineering,financial engineering etc.,which poses a larger challenge for statistical modeling and analysis.Now the research about high-dimensional data is a hot research topic in the current statistics.Based on the theory of Bayesian statistics,combing with classical statistics,the paper has conducted a research on the problem of variable selection and robust estimation for high dimensional linear model.The main content of this paper are as the follows:(1)The research background and status of high-dimensional data were introduced,the research method adopted by this paper was given.(2)The methods of variable selection and parameter estimation for high dimensional linear models were introduced from the perspective of Bayesian statistics and classical statistics respectively,and the relationship between them was analyzed.(3)For the high dimensional linear models,a more robust and efficient method of parameter estimation was proposed.It is a method that combines a log-exp-sum-type penalty with the least-absolute criteria.In the process of parameter estimation,this new method adjusts the weight of the penalty for parameters by themselves so as to get a more robust and accurate result.Numerical simulation test was conducted and the results demonstrated the effectiveness of this new method.(4)The problem of robust parameter estimation for high dimensional linear models was researched based on the theory of Bayesian statistics.In terms of Bayesian Lasso quantile regression model,a method for calculating the likelihood function was proposed based on linear interpolation,then a new sampling algorithm for the posterior distribution was designed by combining prior of the coefficients which is belong to Laplace distribution.Numerical simulation test was conducted for the proposed method and the results demonstrated the robustness and accuracy of this new method for parameter estimation.(5)The influencing factors of return on equity(ROE)of Chinese stock were analyzed by using Bayesian lasso quantile regression method with linear interpolation,regression model about the return on equity(ROE)and the influencing factors was built.Prediction test was carried out for the new model and the results showed its effectiveness.