Mixed-model Bayesian Analysis

Mixture model can be used as the mathematical model in the engineer fields, so the study of mixture model is significant, hi study of theory, there are two problems. One is parameter estimation, the other is estimation of groups number. The method of bayesian analysis is used in the study about mixture model in the thesis, The main work as follows:1. When the number of groups is assumed known, firstly, under particularly prior of parameter, we prove that the bayesian estimation of the normal mixture model parameters is admissibility. Then, MCMC method is applied to deal with the difficult in computing bayesian estimation. The approach is feasible by the success on an example.2. For the problem of label-switching in the mixture model, we give two newly relabeling algorithms and the proof of theory. One is clustering analysis method which relabel for series of parameters estimation through clustering on raw sampler. In another way, we consider undoing the label-switching by making the permuted sample points agree with an inference of statistic. We illustrate the success of our approach on some examples.3. When the number of groups is assumed unknown. Firstly, the "delay rejection" is expanded the variable situation of the parameter's dimension. Then, on the basis of Richardson and Green(1997), we make some modify on "the Reversible Jump MCMC Algorithm". Finally, we discuss "galaxy date" by using the method. Through comparing with their result, we prove our method is more effective.