有限正态总体的贝叶斯预测

发布时间：2018-03-29 21:32

本文选题：Bayes预测　切入点：参数型经验Bayes预测　出处：《东华理工大学》2017年硕士论文

【摘要】：本文研究了有限正态总体中线性数量和二次型数量的贝叶斯预测问题及总体总量的经验Bayes预测问题.第一章,介绍了有限总体模型及其预测问题的研究进展,Bayes方法原理和经验Bayes方法,以及本文的研究意义和结构安排.第二章,主要研究了有限总体中线性数量和二次型数量的贝叶斯预测.首先,在正态-逆伽玛先验和无信息先验下,本文分别给出了总体数量的Bayes预测;其次,本文进一步研究线性数量和二次型数量的贝叶斯预测并得到了它们的Bayes预测风险;最后,本文给出了几个实例来阐明研究的结果.第三章,主要研究了有限正态总体中总体总量的经验贝叶斯预测.首先,基于贝叶斯思想得到了总体总量的贝叶斯预测;其次,考虑到该贝叶斯预测中存在冗余参数,在实际应用中不可行,为此利用历史样本构造了总体总量的参数型经验Bayes预测(PEBP);最后,在均方误差准则下,讨论了总体总量的的PEBP相对于最佳线性无偏预测(BLUP)的优良性.
[Abstract]:In this paper, we study the Bayesian prediction problem of linear quantity and quadratic quantity in finite normal population and the empirical Bayes prediction problem of total population. This paper introduces the research progress of finite population model and its prediction problem. The principle of Bayesian method and empirical Bayes method are introduced, as well as the significance and structure of this paper. This paper mainly studies Bayesian prediction of linear quantity and quadratic quantity in finite population. Firstly, under the condition of normal-inverse gamma priori and no information priori, the Bayes prediction of the total quantity is given respectively. In this paper, we further study the Bayesian prediction of linear quantity and quadratic quantity and obtain their Bayes prediction risks. Finally, we give several examples to illustrate the results of the study. This paper mainly studies the empirical Bayesian prediction of the total population in the finite normal population. Firstly, the Bayesian prediction of the total amount is obtained based on the Bayesian theory; secondly, considering the redundant parameters in the Bayesian prediction, It is not feasible in practical application. For this reason, the parametric empirical Bayes prediction of total population is constructed by using historical samples. Finally, under the mean square error criterion, the superiority of the PEBP of the total population relative to the optimal linear unbiased prediction is discussed.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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