关于此课程： 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.
此课程适用人群： This course is for people interested in learning an alternative to the Frequentist approach that is typically taught in statistics classes. The course covers both concepts and basic computing, and so it is applicable both to people doing data analysis as well as people who read the analysis of others, such as decision makers. This course expects that learners have previous exposure to statistics at the introductory level or higher, and previous exposure to calculus. In both cases, the expectation is that concepts have been seen previously, possibly many years earlier, but that the details may have been forgotten.
教学方： Herbert Lee, Professor
Applied Mathematics and Statistics
| 级别 | 中级 |
| 承诺学习时间 | Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics. |
| 语言 | 英语（English） |
| 如何通过 | 通过所有计分作业以完成课程。 |
| 用户评分 |
- Reading: Module 1 objectives, assignments, and supplementary materials
- Reading: Background for Lesson 1
- 视频: Lesson 1.1 Classical and frequentist probability
- 视频: Lesson 1.2 Bayesian probability and coherence
- Discussion Prompt: Objectivity
- 视频: Lesson 2.1 Conditional probability
- 视频: Lesson 2.2 Bayes' theorem
- Reading: Supplementary material for Lesson 2
- 视频: Lesson 3.1 Bernoulli and binomial distributions
- 视频: Lesson 3.2 Uniform distribution
- 视频: Lesson 3.3 Exponential and normal distributions
- Reading: Supplementary material for Lesson 3
- Reading: Module 2 objectives, assignments, and supplementary materials
- Reading: Background for Lesson 4
- 视频: Lesson 4.2 Likelihood function and maximum likelihood
- 视频: Lesson 4.3 Computing the MLE
- 视频: Lesson 4.4 Computing the MLE: examples
- Reading: Supplementary material for Lesson 4
- 视频: Introduction to R
- 视频: Plotting the likelihood in R
- 视频: Plotting the likelihood in Excel
- Reading: Background for Lesson 5
- 视频: Lesson 5.1 Inference example: frequentist
- 视频: Lesson 5.2 Inference example: Bayesian
- 视频: Lesson 5.3 Continuous version of Bayes' theorem
- 视频: Lesson 5.4 Posterior intervals
- Discussion Prompt: Confidence intervals and credible intervals
- Reading: Supplementary material for Lesson 5
- Reading: Module 3 objectives, assignments, and supplementary materials
- 视频: Lesson 6.2 Prior predictive: binomial example
- 视频: Lesson 6.3 Posterior predictive distribution
- 视频: Lesson 7.1 Bernoulli/binomial likelihood with uniform prior
- 视频: Lesson 7.2 Conjugate priors
- 视频: Lesson 7.3 Posterior mean and effective sample size
- 视频: Data analysis example in R
- 视频: Data analysis example in Excel
- Discussion Prompt: Prior elicitation
- Reading: R and Excel code from example analysis
- 视频: Lesson 8.1 Poisson data
- Reading: Module 4 objectives, assignments, and supplementary materials
- 视频: Lesson 10.1 Normal likelihood with variance known
- 视频: Lesson 10.2 Normal likelihood with variance unknown
- Reading: Supplementary material for Lesson 10
- 视频: Lesson 11.1 Non-informative priors
- 视频: Lesson 11.2 Jeffreys prior
- Discussion Prompt: A non-informative prior
- Reading: Supplementary material for Lesson 11
- Reading: Background for Lesson 12
- 视频: Linear regression in R
- 视频: Linear regression in Excel (Analysis ToolPak)
- 视频: Linear regression in Excel (StatPlus by AnalystSoft)
- Reading: R and Excel code for regression
- 视频: Conclusion
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What I liked in the course is that it focuses on examples and solving actual problems. The quantity and the quality of the lectures is great, but what I really missed is written lectures where one can always lookup forgotten things or read details etc. Also, one thing that I think might be added easily is a reference to Mathematica and Maple's routines. I'm using Maple and it took some efforts to get on track. And finally, I think that 4 quizes per week is really too much for working people. It's true that the tests weren't that difficult, but it took me about an hour to do each, so I think 30 mins of lectures vs. 4 hours of quizzes is a bit unfair. Of course, my background in statistics is non-existent so it may be that it took me longer than average. But I think the course material could have been spread over say 6 weeks for lighter load on the students. All best to the team!
It was my first Bayesian course. Good introduction! However more accent should be placed on intuitive understanding rather than mathematical formalism. To be fair that the issue not only with this course, that the issue with 90% of all stat courses/books. As for me, I find mathematical formalism is hard to digest, intuitive understanding should come first ... May be it's just because of my limited knowledge of stats. I'll update my belief once I get better understanding of stats:) Thank you very much Dr Lee!
Great course for beginners as well as those that need a refresher on the basics!
NJ
Good and clear course. I was impressed by the quality of the material.