Multi - Level Bayesian Model And Its Application

Multilevel Model is an important kind of modeling method for nested structure data, and whose research upsurge originated from the 1990 s. Currently, Multilevel Model has been widely applied in many fields such as Education, Sociology, Economics, Geography, etc. Bayesian statistical theory originated in a paper of the British Statistician named Thomas Bayes in 1763, which has occupied an important position in all the areas of statistics after the development of the 20 th century. It is the application of the theory and method for Bayesian Statistics in Multilevel Model of statistical inference that has become a hot frontier of statistics science.The paper is based on the domestic and foreign scholars’ research. Not only it carry on the preliminary comb for the basic theory of the Multilevel Model and Bayesian Method, but also apply Bayesian Statistical Inference Method of Multilevel Model in the study of factors affecting for the income and growth of farmers in Hong He Prefecture of Yunnan Province.The main research contents are as follows:First of all, it systematically sorted out that the basic method of Multi-level Bayesian Linear Model, and a detailed proof of the proposition is given for the method of conjugate prior distribution of parameters in Multilevel Model.Secondly, for the data structure of the income of farmers in Hong He Prefecture of Yunnan Province, we construct the Bayesian Statistical Inference of three-level of factors affecting the income of farmers. We discuss the research of Bayesian Statistical Inference based on three-level model, and in the comparative research of statistical inference of Empirical Bayesian and Fully Bayesian, it is concluded that the fully Bayesian statistical inference of three-level has obvious advantages.Finally, in order to apply Multilevel Development Model of the Bayesian Statistical Inference to explore the factors influencing the growth of the income of farmers in Hong He Prefecture of Yunnan Province and analyze the problems, we should construct the development model of the three or four levels. In the comparative study based on the development model of two, three, and four level, it is concluded that the three level Bayesian Development Model has obvious advantages direct to the factors influencing the growth of the income.Above all, this paper fully demonstrated the advantages of multi-level model for the high-level nested data, and the significant effect of Bayesian inference in a small number of high-level data units or unbalanced.