貝葉斯統(tǒng)計理論的形成及發(fā)展
發(fā)布時間：2018-07-25 19:43
【摘要】：在數(shù)理統(tǒng)計中，貝葉斯學派已發(fā)展為一個有影響的學派．時至今日，其影響日益擴大．本文通過對相關典籍的研讀，采用史料分析法．比較研究法．在前人已有工作的基礎上，對貝葉斯理論進行了較為詳細的考證和研究．主要工作如下： 一、詳細考證了貝葉斯的研究工作，在釋讀貝葉斯的奠基性原文基礎上，重點分析了貝葉斯如何提出貝葉斯理論，，貝葉斯公式、貝葉斯假設，以及《機會學說中一個問題的解》的開創(chuàng)性意義． 二、對拉普拉斯的一篇文章《論事件原因存在的概率》進行了詳細研究，拉普拉斯獨立的在這篇文章中提出了與貝葉斯理論一致的＂不充分推理原則＂．本論文通過對貝葉斯和拉普拉斯的方法進行比較，揭示了這兩種方法的區(qū)別． 三、介紹了20世紀貝葉斯理論的確認，以及后續(xù)的發(fā)展、應用．對貝葉斯理論從產(chǎn)生到發(fā)展的歷史脈絡進行了梳理． 四、對貝葉斯學派和經(jīng)典學派在概率的解釋、統(tǒng)計推斷中信息選擇和隨機變量的認識三方面的差異進行了比較．分析了貝葉斯學派和經(jīng)典學派的優(yōu)缺點．
[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.
【學位授予單位】：山西師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.8
本文編號：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.
【學位授予單位】：山西師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.8
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