贝叶斯统计理论的形成及发展
发布时间：2018-07-25 19:43
【摘要】：在数理统计中，贝叶斯学派已发展为一个有影响的学派．时至今日，其影响日益扩大．本文通过对相关典籍的研读，采用史料分析法．比较研究法．在前人已有工作的基础上，对贝叶斯理论进行了较为详细的考证和研究．主要工作如下： 一、详细考证了贝叶斯的研究工作，在释读贝叶斯的奠基性原文基础上，重点分析了贝叶斯如何提出贝叶斯理论，，贝叶斯公式、贝叶斯假设，以及《机会学说中一个问题的解》的开创性意义． 二、对拉普拉斯的一篇文章《论事件原因存在的概率》进行了详细研究，拉普拉斯独立的在这篇文章中提出了与贝叶斯理论一致的＂不充分推理原则＂．本论文通过对贝叶斯和拉普拉斯的方法进行比较，揭示了这两种方法的区别． 三、介绍了20世纪贝叶斯理论的确认，以及后续的发展、应用．对贝叶斯理论从产生到发展的历史脉络进行了梳理． 四、对贝叶斯学派和经典学派在概率的解释、统计推断中信息选择和随机变量的认识三方面的差异进行了比较．分析了贝叶斯学派和经典学派的优缺点．
[Abstract]:In mathematical statistics, Bayesian school has developed into an influential school. Today, the influence of Bayesian school is increasing. Through the study of relevant books and books, this paper adopts the method of historical data analysis and comparative research. On the basis of the previous work, The main work of this paper is as follows: first, the research work of Bayes is studied in detail, which is based on the interpretation of the basic text of Bayes. The significance of how Bayes put forward Bayesian theory, Bayesian formula, Bayesian hypothesis and the solution of a problem in the theory of opportunity is analyzed. A detailed study of Laplace's article on the probability of the cause of events, Laplacas has put forward the "inadequate reasoning principle" which is consistent with Bayesian theory in this paper. By comparing Bayesian and Laplace's methods, this paper reveals the differences between these two methods. This paper introduces the confirmation of Bayesian theory in the 20th century, and its subsequent development and application. It combs the historical context of Bayesian theory from its origin to development. Fourthly, it explains the probability of Bayesian school and classical school. The differences between information selection and cognition of random variables in statistical inference are compared, and the advantages and disadvantages of Bayesian school and classical school are analyzed.
【学位授予单位】：山西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.8
本文编号：2144874
[Abstract]:In mathematical statistics, Bayesian school has developed into an influential school. Today, the influence of Bayesian school is increasing. Through the study of relevant books and books, this paper adopts the method of historical data analysis and comparative research. On the basis of the previous work, The main work of this paper is as follows: first, the research work of Bayes is studied in detail, which is based on the interpretation of the basic text of Bayes. The significance of how Bayes put forward Bayesian theory, Bayesian formula, Bayesian hypothesis and the solution of a problem in the theory of opportunity is analyzed. A detailed study of Laplace's article on the probability of the cause of events, Laplacas has put forward the "inadequate reasoning principle" which is consistent with Bayesian theory in this paper. By comparing Bayesian and Laplace's methods, this paper reveals the differences between these two methods. This paper introduces the confirmation of Bayesian theory in the 20th century, and its subsequent development and application. It combs the historical context of Bayesian theory from its origin to development. Fourthly, it explains the probability of Bayesian school and classical school. The differences between information selection and cognition of random variables in statistical inference are compared, and the advantages and disadvantages of Bayesian school and classical school are analyzed.
【学位授予单位】：山西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.8
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