Studying On Selecting Theory Of Prior Distribution

The establishment of the prior distribution is most important for Bayesian statistics,which contains two aspects , one is how to establish the prior distribution of parameters by a bit of non-information or prior information, the other is how to choose a proper prior distribution from so many ones. A criterion of classifying for these methods for the first problem is proposed in this paper which has been discussed by many Bayesian statisticalists. According different applications to the information we collect and category these methods which are used usually and introduce a new notion—prior under the control of the dates in order to clarify the conceptions between non-informative prior and non-subjective prior.A basic idea is expressed for choosing prior distribution, which is same to the choice of parameter for the model in the space of parameters. A set of theory for this is built in virtue of classical statistics in this paper and a verification for that is given. And then the ways of prior selection which utilizes prior information only is proposed. The verification for that hierarchical Bayesian prior is a kind of reasonable prior means indicate that the method establishing hierarchical Bayesian prior of prior is a proper method to chose prior. This is a new application to hierarchical Bayesian prior.At last, methods to choose prior resort Bayesian analysis are given from two aspects. Numerations of posterior distribution to gain prior distribution and parameter is given respectively, the corresponding method to choose prior is educed consequently. At the same time we conclude that Bayesian likelihood reasonable prior and posterior likelihood reasonable prior are uniform with classical ML--II prior when the distribution of prior is equal distribution.