Acerca de este curso: 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.
Para quién es esta clase: 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.
Enseñado por: Herbert Lee, Professor
Applied Mathematics and Statistics
| Nivel | Intermedio |
| Compromiso | Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics. |
| Idioma | English |
| Cómo aprobar | Aprueba todas las tareas calificadas para completar el curso. |
| Calificaciones del usuario |
- Reading: Module 1 objectives, assignments, and supplementary materials
- Reading: Background for Lesson 1
- Vídeo: Lesson 1.1 Classical and frequentist probability
- Vídeo: Lesson 1.2 Bayesian probability and coherence
- Discussion Prompt: Objectivity
- Vídeo: Lesson 2.1 Conditional probability
- Vídeo: Lesson 2.2 Bayes' theorem
- Reading: Supplementary material for Lesson 2
- Vídeo: Lesson 3.1 Bernoulli and binomial distributions
- Vídeo: Lesson 3.2 Uniform distribution
- Vídeo: 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
- Vídeo: Lesson 4.2 Likelihood function and maximum likelihood
- Vídeo: Lesson 4.3 Computing the MLE
- Vídeo: Lesson 4.4 Computing the MLE: examples
- Reading: Supplementary material for Lesson 4
- Vídeo: Introduction to R
- Vídeo: Plotting the likelihood in R
- Vídeo: Plotting the likelihood in Excel
- Reading: Background for Lesson 5
- Vídeo: Lesson 5.1 Inference example: frequentist
- Vídeo: Lesson 5.2 Inference example: Bayesian
- Vídeo: Lesson 5.3 Continuous version of Bayes' theorem
- Vídeo: 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
- Vídeo: Lesson 6.2 Prior predictive: binomial example
- Vídeo: Lesson 6.3 Posterior predictive distribution
- Vídeo: Lesson 7.1 Bernoulli/binomial likelihood with uniform prior
- Vídeo: Lesson 7.2 Conjugate priors
- Vídeo: Lesson 7.3 Posterior mean and effective sample size
- Vídeo: Data analysis example in R
- Vídeo: Data analysis example in Excel
- Discussion Prompt: Prior elicitation
- Reading: R and Excel code from example analysis
- Vídeo: Lesson 8.1 Poisson data
- Reading: Module 4 objectives, assignments, and supplementary materials
- Vídeo: Lesson 10.1 Normal likelihood with variance known
- Vídeo: Lesson 10.2 Normal likelihood with variance unknown
- Reading: Supplementary material for Lesson 10
- Vídeo: Lesson 11.1 Non-informative priors
- Vídeo: Lesson 11.2 Jeffreys prior
- Discussion Prompt: A non-informative prior
- Reading: Supplementary material for Lesson 11
- Reading: Background for Lesson 12
- Vídeo: Linear regression in R
- Vídeo: Linear regression in Excel (Analysis ToolPak)
- Vídeo: Linear regression in Excel (StatPlus by AnalystSoft)
- Reading: R and Excel code for regression
- Vídeo: Conclusion
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Very well taught and informative.
I think the course would benefit by recommending a textbook that would supplement the lecture material. It's nice to have a reference to refer to after viewing the lectures.
This course strikes a perfect balance between not being too simple or too slow on one hand, and offering an easily accessible introduction to many central topic of Bayesian statistics on the other.
I think that good knowledge of basic probability theory and one-variable calculus is necessary for getting the maximum out of this course. This, however, is strictly due to the probabilistic underpinnings of the Bayesian theory.
MD
the notes for the lectures are missing.
In my opinion the notes, which includes the video materials could be very useful.
the course was good. I learnt some new concepts in bayesian thinking.