About this course: 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.
Who is this class for: 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.
Taught by: Herbert Lee, Professor
Applied Mathematics and Statistics
| Level | Intermediate |
| Commitment | Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics. |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
- Video: Course introduction
- Reading: Module 1 objectives, assignments, and supplementary materials
- Reading: Background for Lesson 1
- Video: Lesson 1.1 Classical and frequentist probability
- Video: Lesson 1.2 Bayesian probability and coherence
- Discussion Prompt: Objectivity
- Video: Lesson 2.1 Conditional probability
- Video: Lesson 2.2 Bayes' theorem
- Reading: Supplementary material for Lesson 2
- Video: Lesson 3.1 Bernoulli and binomial distributions
- Video: Lesson 3.2 Uniform distribution
- Video: 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
- Video: Lesson 4.1 Confidence intervals
- Video: Lesson 4.2 Likelihood function and maximum likelihood
- Video: Lesson 4.3 Computing the MLE
- Video: Lesson 4.4 Computing the MLE: examples
- Reading: Supplementary material for Lesson 4
- Video: Introduction to R
- Video: Plotting the likelihood in R
- Video: Plotting the likelihood in Excel
- Reading: Background for Lesson 5
- Video: Lesson 5.1 Inference example: frequentist
- Video: Lesson 5.2 Inference example: Bayesian
- Video: Lesson 5.3 Continuous version of Bayes' theorem
- Video: 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
- Video: Lesson 6.1 Priors and prior predictive distributions
- Video: Lesson 6.2 Prior predictive: binomial example
- Video: Lesson 6.3 Posterior predictive distribution
- Video: Lesson 7.1 Bernoulli/binomial likelihood with uniform prior
- Video: Lesson 7.2 Conjugate priors
- Video: Lesson 7.3 Posterior mean and effective sample size
- Video: Data analysis example in R
- Video: Data analysis example in Excel
- Discussion Prompt: Prior elicitation
- Reading: R and Excel code from example analysis
- Video: Lesson 8.1 Poisson data
- Reading: Module 4 objectives, assignments, and supplementary materials
- Video: Lesson 9.1 Exponential data
- Video: Lesson 10.1 Normal likelihood with variance known
- Video: Lesson 10.2 Normal likelihood with variance unknown
- Reading: Supplementary material for Lesson 10
- Video: Lesson 11.1 Non-informative priors
- Video: Lesson 11.2 Jeffreys prior
- Discussion Prompt: A non-informative prior
- Reading: Supplementary material for Lesson 11
- Reading: Background for Lesson 12
- Video: Linear regression in R
- Video: Linear regression in Excel (Analysis ToolPak)
- Video: Linear regression in Excel (StatPlus by AnalystSoft)
- Reading: R and Excel code for regression
- Video: Conclusion
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Very straight-to-the-point course. Very dense, though, for a newbe in bayesian terms and concepts. But I definitely suggest it to undertand priors and posterior concepts. Thanks!
Very well structured course. Problems and quiz are real life problems, and it's challenging and rewarding to solve them. Thanks to Prof. Lee for delivering an awesome course.
This is a decent course that covers an important topic that I've had a trouble finding good resources for learning about.
Pros: comprehensive coverage of the topic at a high level.
Cons: not enough examples to understand what is talked about in the lectures (especially the continuous data and prior with normal distribution lectures) and to anchor the topic in its practical uses.
I recommend supplementing this course with the MIT OCW 18-05 statistics class (I actually put this on hold and did that then came back).
If this course had a lot more practice problems with fully worked out answers it would help tremendously. I understand a sequel to this class is in the works and I look forward to taking it.
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DM
Satisfied with the course in general. Good investment of my time!!