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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/bayesian-statistics
课程评论：没有评论
课程名称：贝叶斯统计：从概念到数据分析 课程概述：本课程介绍了贝叶斯统计方法，从概率概念出发，逐步深入数据分析。我们将学习贝叶斯方法的哲学，并了解如何对常见类型的数据进行实现。课程中将比较贝叶斯方法与更常见的频率学派方法，探讨贝叶斯方法的一些优势，特别是它在处理不确定性方面的优势、更直观易懂的结果以及更明确的假设陈述。本课程结合了讲座视频、计算机演示、阅读材料、练习和讨论板，创造一个积极的学习体验。在计算方面，您可以选择使用Microsoft Excel或开放源代码的免费统计软件R，两个选项的内容相当。讲座将提供一些基本的数学发展以及哲学和解释的讲解。完成本课程后，您将理解贝叶斯方法的概念、掌握贝叶斯与频率学派的关键区别，并具备进行基本数据分析的能力。 课程大纲： 1. 概率与贝叶斯定理 - 该模块回顾概率的基本知识和贝叶斯定理。课程将介绍概率的不同范式或定义，并讨论为何概率为处理不确定性提供了一个一致的框架。课程还将回顾条件概率的规则，并介绍贝叶斯定理，最后回顾离散和连续随机变量的常见概率分布。 2. 统计推断 - 本模块从频率学派和贝叶斯的视角介绍统计推断的概念。课程将展示频率学派的最大似然估计和二项数据的置信区间，同时介绍贝叶斯推断的基本原理，通过贝叶斯定理将先验概率与数据结合，获得后验概率。该框架还扩展到连续版本的贝叶斯定理，以估算连续模型参数并计算后验概率和可信区间。 3. 离散数据的先验与模型 - 本模块将学习选择先验分布和构建离散数据模型的方法。课程介绍先验选择和预测分布，以评估先验的有效性。通过对伯努利数据的贝叶斯分析，介绍计算上便利的共轭先验，构建泊松数据的共轭模型，并讨论先验超参数的选择策略。 4. 连续数据的模型 - 本模块涵盖对连续数据的共轭与客观贝叶斯分析。展示指数分布数据的共轭模型，讨论正态分布数据（在统计学中扮演重要角色）的模型。同时，回顾先验选择的问题，并讨论“客观”或“非信息性”先验。最后，介绍具有非信息性先验的贝叶斯线性回归模型，其结果与经典回归相当。 通过学习本课程，学员能够深入理解贝叶斯统计的基本概念与应用。
Name:Probability and Bayes' Theorem
Description:In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
Name:Statistical Inference
Description:This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.
Name:Priors and Models for Discrete Data
Description:In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.
Name:Models for Continuous Data
Description:This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.
This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.
