|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/bayesian-statistics-and-credibility-theory/
课程评论：没有评论
课程名称：贝叶斯统计与可靠性理论 课程概述：本短期课程旨在满足精算考试的课程目标，主要包括以下内容： 1. 解释贝叶斯统计的基本概念，并运用这些概念计算贝叶斯估计器。 2. 利用贝叶斯定理计算简单条件概率。 3. 解释先验分布、后验分布和共轭先验分布的含义。 4. 在简单案例中推导参数的后验分布。 5. 解释损失函数的含义，并利用简单的损失函数推导参数的贝叶斯估计。 6. 解释可靠性溢价公式的涵义，并描述可靠性因子所起的作用。 7. 说明贝叶斯方法在可靠性理论中的应用，并运用其在简单情况下推导可靠性溢价。 8. 解释经验贝叶斯方法在可靠性理论中的应用，并用其在简单情况中推导可靠性溢价。 9. 说明这两种方法之间的区别，并阐述每种方法所基于的假设。 本课程将帮助学员掌握贝叶斯统计和可靠性理论的核心概念，应用于实际问题中。
This short course aims to address the following syllabus objectives of the Actuarial Exams:Explain the fundamental concepts of Bayesian statistics and use these concepts to calculate Bayesian estimators. Use Bayes' theorem to calculate simple conditional probabilities. Explain what is meant by a prior distribution, a posterior distribution and a conjugate prior distribution.Derive the posterior distribution for a parameter in simple cases. Explain what is meant by a loss function. Use simple loss functions to derive Bayesian estimates of parameters. Explain what is meant by the credibility premium formula and describe the role played by the credibility factor. Explain the Bayesian approach to credibility theory and use it to derive credibility premiums in simple cases. Explain the empirical Bayes approach to credibility theory and use it to derive credibility premiums in simple cases. Explain the differences between the two approaches and state the assumptions underlying each of them.
