Study On The HPD Credible Sets And The Admissible Estimation

The Bayesian statistical theory has been accepted by the more and more statistical scholar with its special visual angle and view. It makes solving some difficult problems in classical statistical theory possible and has become the one of most important school of though of statistics. We make the simple view to the development, history and principal views of the Bayesian statistical theory in the first chapter.The second chapter generates the methods of obtaining the prior and posterior distribution. The conjugate prior distributions of some particular distributions are provided.The third chapter generates the method of obtaining the highest posterior density (HPD) credible set. A new method based on computational geometry for computing the HPD credible set is presented. We compare the HPD credible set and the classical confidence set. The results show that the HPD credible set is better than its classical counterpart; it is easier to interpret than the classical confidence set and is shorter than the classical confidence set.Finally, in the fourth chapter, we discuss the admissibility of estimations on the distributions of one-parameter exponential family.