Hierachical Model With Bayesian Methods

Bayesian method based on Bayes’ theorm is developed for elavorating systemlyand solving statistical problems. The basic approach is to obtain posterioriinformation with the combination of the priori information about the unknownparameters and sample information according to Bayes’ theorm. The advantage of thismethod is avoiding the drawbacks that the size is too small in the classical distribution.There’re so many ways applied to approximate a posteriori quantity including MonteCarlo sample and Gibbs sample under the conditions of conjugate prior, theM-algorithm and MH-algorithm without the assumption.In social science research, we usually sample from different levels and units andthen the data brings lots of interesting cross-level research questions. Thehierarchical model is a useful analytical tool for sparse data. For example, whenwe’re studying on the scores of a grade children between schools, if the sample sizeof a school is too small to provide enough information for assessing the result, butthe hierarchical statistical analysis model can take advantage of all the scool data tocompensate for the problem about sparse data of individual school in the sample.In this paper we mainly discuss the hierarchical model and the hierarchicallinear model under the Bayesian approach. Such a model parameter estimation cannot only use the sub-samples of each group, but also take advantage of theinformation about all of the groups. It can support the statistical estimation of thegroups containing less information in terms of the total information from all of thegroups. In practical study, the differences of sub-sample size between groups may beso large that sub-sample size is very small. This study is suitable for such datastatistical analysis.