About this course: This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction. We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."
Created by: Duke University
Taught by: Mine Çetinkaya-Rundel, Associate Professor of the Practice
Department of Statistical Science
Taught by: David Banks, Professor of the Practice
Statistical Science
Taught by: Colin Rundel , Assistant Professor of the Practice
Statistical Science
Taught by: Merlise A Clyde, Professor
Department of Statistical Science
| Basic Info | Course 4 of 5 in the Statistics with R Specialization |
| Level | Intermediate |
| Commitment | 5 weeks of study, 5-7 hours/week |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
About the Specialization and the Course
This short module introduces basics about Coursera specializations and courses in general, this specialization: Statistics with R, and this course: Bayesian Statistics. Please take several minutes read this information. Thanks for joining us in this course!
1 video, 4 readings
- Reading: About Statistics with R Specialization
- Reading: About Bayesian Statistics
- Reading: Special Thanks
- Reading: Weekly Feedback Forms
- Discussion Prompt: Introduce Yourself
The Basics of Bayesian Statistics
<p>Welcome! Over the next several weeks, we will together explore Bayesian statistics. <p>In this module, we will work with conditional probabilities, which is the probability of event B given event A. Conditional probabilities are very important in medical decisions. By the end of the week, you will be able to solve problems using Bayes' rule, and update prior probabilities.</p><p>Please use the learning objectives and practice quiz to help you learn about Bayes' Rule, and apply what you have learned in the lab and on the quiz.
9 videos, 3 readings, 1 practice quiz
- Reading: Module Learning Objectives
- Video: Conditional Probabilities and Bayes' Rule
- Video: Bayes' Rule and Diagnostic Testing
- Video: Bayes Updating
- Video: Bayesian vs. frequentist definitions of probability
- Video: Inference for a Proportion: Frequentist Approach
- Video: Inference for a Proportion: Bayesian Approach
- Video: Effect of Sample Size on the Posterior
- Video: Frequentist vs. Bayesian Inference
- Practice Quiz: Week 1 Practice Quiz
- Reading: Week 1 Lab Instructions
- Reading: Week 1 Feedback Form
Graded: Week 1 Quiz
Graded: Week 1 Lab
WEEK 2
Bayesian Inference
In this week, we will discuss the continuous version of Bayes' rule and show you how to use it in a conjugate family, and discuss credible intervals. By the end of this week, you will be able to understand and define the concepts of prior, likelihood, and posterior probability and identify how they relate to one another.
10 videos, 3 readings, 1 practice quiz
- Reading: Module Learning Objectives
- Video: From the Discrete to the Continuous
- Video: Elicitation
- Video: Conjugacy
- Video: Inference on a Binomial Proportion
- Video: The Gamma-Poisson Conjugate Families
- Video: The Normal-Normal Conjugate Families
- Video: Non-Conjugate Priors
- Video: Credible Intervals
- Video: Predictive Inference
- Practice Quiz: Week 2 Practice Quiz
- Reading: Week 2 Lab Instructions
- Reading: Weekly Feedback Form
Graded: Week 2 Quiz
Graded: Week 2 Lab
WEEK 3
Decision Making
In this module, we will discuss Bayesian decision making, hypothesis testing, and Bayesian testing. By the end of this week, you will be able to make optimal decisions based on Bayesian statistics and compare multiple hypotheses using Bayes Factors.
12 videos, 3 readings, 1 practice quiz
- Reading: Module Learning Objectives
- Video: Losses and decision making
- Video: Working with loss functions
- Video: Minimizing expected loss for hypothesis testing
- Video: Posterior probabilities of hypotheses and Bayes factors
- Video: Comparing two proportions using Bayes factors: assumptions
- Video: Comparing two proportions using Bayes factors
- Video: Comparing two paired means using Bayes factors
- Video: What to report?
- Video: Posterior probability, p-values and paradoxes
- Video: Comparing two independent means
- Video: Comparing two independent means: hypothesis testing
- Practice Quiz: Week 3 Practice Quiz
- Reading: Week 3 Lab Instructions
- Reading: Weekly Feedback Form
Graded: Week 3 Quiz
Graded: Week 3 Lab
WEEK 4
Bayesian Regression
This week, we will look at Bayesian linear regressions and model averaging, which allows you to make inferences and predictions using several models. By the end of this week, you will be able to implement Bayesian model averaging, interpret Bayesian multiple linear regression and understand its relationship to the frequentist linear regression approach.
11 videos, 4 readings, 1 practice quiz
- Reading: Module Learning Objectives
- Video: Bayesian simple linear regression
- Video: Checking for outliers
- Video: Bayesian multiple regression
- Video: Model selection criteria
- Video: Bayesian model uncertainty
- Video: Bayesian model averaging
- Video: Stochastic exploration
- Video: Priors for Bayesian model uncertainty
- Video: R demo: crime and punishment
- Video: Decisions under model uncertainty
- Practice Quiz: Week 4 Practice Quiz
- Reading: Week 4 Lab Instructions
- Reading: Week 4 Lab Supplement
- Reading: Weekly Feedback Form
Graded: Week 4 Quiz
Graded: Week 4 Lab
WEEK 5
Perspectives on Bayesian Applications
This week consists of interviews with statisticians on how they use Bayesian statistics in their work, as well as the final project in the course.
3 videos, 2 readings
- Reading: About this module
- Video: Bayesian methods and big data: a talk with David Dunson
- Video: Bayesian methods in biostatistics and public health: a talk with Amy Herring
- Reading: Weekly Feedback Form
Data Analysis Project
In this module you will use the data set provided to complete and report on a data analysis question. Please read the background information, review the report template (downloaded from the link in Lesson Project Information), and then complete the peer review assignment.
2 readings
- Reading: Project information
- Reading: Weekly Feedback Form
Graded: Data Analysis Project
FAQs
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| Access to course materials | Available |
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Ratings and Reviews
This is course is very intuitive!
I like this course a lot. Explanations are clear and much of the (unnecessarily heavyweight) maths is glossed over. I particularly liked the sections on Bayesian model selection.
Strongly recommend!
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Thanks!