贝叶斯统计简介11.11

课程编号：

课程名称（中文）： 贝叶斯统计

课程名称（英文）： Bayesian Statistics

学分数/学时数： 4/4

开课单位/开课学期： 数学与计算科学学院/5-7

课程类别： 选修课

面向专业：

课程负责人：

课程内容简介（中文）：

课程内容简介（英文）：

贝叶斯统计简介

经典统计学的一个主要内容是对分布族的参数进行估计和检验，其中的参数是被看作是一个未知的固定的量。经典统计学直接利用样本信息进行推断，不考虑关于参数的非样本信息信息（例如参数的先验信息，推断可能带来的后果)。贝叶斯推断把先验信息正式地纳入统计学中并利用这种信息,把参数看作可以用先验分布来描述的随机变量。贝叶斯决策还进一步引入损失函数，把推断与经济上的得失联系起来，更便于用在经济决策领域。

课程的内容主要包括：先验分布与后验分布；先验分布的确定；贝叶斯推断；函数和损失函数；贝叶斯决策。通过本课程的学习可以使学生掌握贝叶斯统计的基本理论和应用。

修习本课程的学生需要具有概率统计的知识。

A Brief Introduction to Bayesian Statistics

Point estimation and hypothesis testing about parameters are the major subjects in classical statistics, and the parameter is thought to be an unknown, but fixed, quantity. Classical statistics is directed towards the use of the sample information in making inference about the parameter, without regard to the nonsample information, such as the prior information about the parameter, and possible consequences of the reference. Bayesian inference utilize prior information formally. And Bayesian decision theory introduces also the loss function into the statistical field, with the loss function one can connect the reference with the economical loss, so that the Bayesian theory can more easily apply to the economic fields.

The main contents of the course are as follows: prior distribution and posterior distribution, the determination of the prior distribution, Bayesian inference, utility function and loss function, Bayesian decision. The students can learn the basic Bayesian theory and its application from this course.

Probability and statistics are required for this course.