Bayesian Discriminant Method Based On Semiparametric Density Ratio Model

Density ratio models are a type of important semiparametric models and a hot topic for statisticians.Both populations being normally is a traditional and important statistical hypothesis on which many basically statistical methods are developed.However,after the density ratio model is proposed,we have a looser version than traditional hypothesis that the ratio of two density functions conforms to the density ratio model.Therefore,the parametric statistics methods based on the normally distributed hypothesis developed the corresponding semi-parametric version gradually.The traditional bayesian discriminant method assumes that the samples are taken from normal distributions which have the same covariance matrix so as to facilitate the calculation in practice.Traditional beyesian discrimination belongs to the parametric method,it may not achieve a good discriminant effect under the complex realistic data.Therefore,we propose a semiparametric bayesian discrimination based on density ratio model.This new method can analyse more complex real data.The results of statistical simulation show the following conclusion: under the density ratio model,if each of group is normal distribution,the discriminant effect of the new method is equal to that of the traditional method;otherwise,the new method is obviously better than the traditional method.We use the new method to analyse four groups of real cases and give the discriminant results.Chapter one,we summarize the practical significance and innovation points of this topic,and introduce theresearch backgroud and the development status of this field.Chapter two,the density ratio model and the traditional bayesian method are introduced.Then,the semiparametric bayesian discriminant method is established.Finally,the parameter estimators and the goodness of fit test method are given under the empirical likelihood method.Chapter three,we introduce the design and procedure of statistical simulation experiment.Then,the common distributions included in the density ratio model is discussed.Finally,the simulation results based on five different conditions are obtained.Chapter four,four groups of real cases are analysed by the traditional and new methods.Chapter five,we summarize the advantage of semiparametric bayesian discriminant method.