【作者】 华鹏；

【导师】 刘福升；

【作者基本信息】 山东科技大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 本文对贝叶斯决策理论作了探讨。首先，简要介绍了与贝叶斯决策有关的基本要素和基本原理以及贝叶斯最优决策的准则。对贝叶斯决策的稳健性作出了进一步探讨，讨论了ε-代换类的贝叶斯稳健性。本文对贝叶斯假设检验进行了研究，讨论了经验贝叶斯双边假设检验问题，对一个离散的指数族，构造了一个经验贝叶斯检验统计量，并着重证明了所给出统计量的渐进最优性。此外，本文还探讨了模型选择问题，首先介绍了贝叶斯因子和决策理论框架下的模型选择问题，进而给出了一种模型选择的新方法—期望—后验先验分布法，结合贝叶斯因子法对模型选择问题进行了讨论。更多还原

【Abstract】 In this paper, we discuss the theory of Bayesian decision. Firstly, I introduce the basic factors and theory about the Bayesian decision. Secondly, we consider further the problem of measuring Bayesian robustness, and discuss the classes of contaminated prior in specific. Thirdly, we deal with the problem of testing H0 :[1,2],H1 :[1,2], where 0<1 <2 < , for the parameter in adiscrete exponential family via the empirical Bayes approach, construct the empirical Bayes test by resembling the behavior of the Bayes test, investigate the asymptotic optimality of the empirical Bayes test. Finally we consider the problem of comparing parameter models using a Bayesian approach and decision theory. A new method of developing prior distribution for the model parameter is presented, called the expected-posterior prior approach.更多还原