基于后验预测分布的Bayes推断及相关问题研究

项目名称： 基于后验预测分布的Bayes推断及相关问题研究

项目编号： No.11201005

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 何道江

作者单位： 安徽师范大学

项目金额： 22万元

中文摘要： 本项目旨在基于Bayes统计的思想和方法来研究一些重要的假设检验问题。研究内容分为三个部分：一是构造Bayes框架下的似然比统计量，提示相应的Wilks现象以及优良性质，并研究其在统计推断中的应用；二是基于Bayes来研究拟合优度检验问题，构造新的检验方法，重点使得检验功效能够得到显著提高；三是研究Bayes推断与频率推断的和谐性问题，重点研究Bayes证据和频率证据的一致性。项目研究问题横跨频率统计和Bayes统计两大学派，研究内容既有统计学中基础性的理论问题，也有统计学相关应用领域中具有重要应用价值的问题。因此，本项目的研究不仅具有重要的理论意义和学术价值，而且也有广阔的应用前景。

中文关键词： 后验预测分布；后验预测p-值；经验Bayes；客观Bayes；Cholesky分解

英文摘要： This project aims to investigate some important statistical hypothesis testing problems based on Bayesian paradigm. The proposal is made up of three parts. First, we will construct Bayesian analogue of the likelihood ratio statistic in frequentist statistics, unveil the corresponding Wilks phenomenon, and develop the applications in statistical inference. Second, we will propose new Bayesian goodness-of-fit test approaches. The key point is to improve the power of the test significantly. Third, we will study the reconciliation between the Bayesian inference and the frequentist inference. The emphasis is put on the agreement between the Bayesian evidence and the frequentist evidence. The problems we considered link the frequentist statistics and Bayesian statistics. The proposal involves fundamental problems in statistics as well as practical problems in application. Therefore, this project is not only of theoretical importance, but also of promising value in application.

英文关键词： posterior predictive distribution；posterior predictive p value；empirical Bayes；objective Bayes；Cholesky decompostion