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Bayesian Statistics

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Bayesian Statistics

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Gain insight into a topic and learn the fundamentals.
3.8

799 reviews

Intermediate level
Some related experience required
Flexible schedule
4 weeks at 10 hours a week
Learn at your own pace
79%
Most learners liked this course
Gain insight into a topic and learn the fundamentals.
3.8

799 reviews

Intermediate level
Some related experience required
Flexible schedule
4 weeks at 10 hours a week
Learn at your own pace
79%
Most learners liked this course

Build your subject-matter expertise

This course is part of the Data Analysis with R Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
  • Learn new concepts from industry experts
  • Gain a foundational understanding of a subject or tool
  • Develop job-relevant skills with hands-on projects
  • Earn a shareable career certificate

There are 7 modules in 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."

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!

What's included

1 video5 readings

1 video•Total 2 minutes
  • Introduction to Statistics with R•2 minutes
5 readings•Total 37 minutes
  • About Statistics with R Specialization•10 minutes
  • About Bayesian Statistics•10 minutes
  • Pre-requisite Knowledge•10 minutes
  • Special Thanks•2 minutes
  • Report a problem with the course•5 minutes

<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.

What's included

9 videos4 readings3 assignments

9 videos•Total 41 minutes
  • The Basics of Bayesian Statistics•2 minutes
  • Conditional Probabilities and Bayes' Rule•2 minutes
  • Bayes' Rule and Diagnostic Testing•7 minutes
  • Bayes Updating•3 minutes
  • Bayesian vs. frequentist definitions of probability•4 minutes
  • Inference for a Proportion: Frequentist Approach•4 minutes
  • Inference for a Proportion: Bayesian Approach•8 minutes
  • Effect of Sample Size on the Posterior•2 minutes
  • Frequentist vs. Bayesian Inference•10 minutes
4 readings•Total 260 minutes
  • Module Learning Objectives•120 minutes
  • About Lab Choices•10 minutes
  • Week 1 Lab Instructions (RStudio)•120 minutes
  • Week 1 Lab Instructions (RStudio Cloud)•10 minutes
3 assignments•Total 80 minutes
  • Week 1 Practice Quiz•20 minutes
  • Week 1 Lab•30 minutes
  • Week 1 Quiz•30 minutes

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.

What's included

10 videos3 readings3 assignments

10 videos•Total 45 minutes
  • Bayesian Inference•2 minutes
  • From the Discrete to the Continuous•5 minutes
  • Elicitation•6 minutes
  • Conjugacy•4 minutes
  • Inference on a Binomial Proportion•5 minutes
  • The Gamma-Poisson Conjugate Families•6 minutes
  • The Normal-Normal Conjugate Families•4 minutes
  • Non-Conjugate Priors•4 minutes
  • Credible Intervals•4 minutes
  • Predictive Inference•4 minutes
3 readings•Total 310 minutes
  • Module Learning Objectives•120 minutes
  • Week 2 Lab Instructions (RStudio)•180 minutes
  • Week 1 Lab Instructions (RStudio Cloud)•10 minutes
3 assignments•Total 90 minutes
  • Week 2 Practice Quiz•20 minutes
  • Week 2 Lab•30 minutes
  • Week 2 Quiz•40 minutes

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.

What's included

14 videos3 readings3 assignments

14 videos•Total 75 minutes
  • Decision making•1 minute
  • Losses and decision making•3 minutes
  • Working with loss functions•7 minutes
  • Minimizing expected loss for hypothesis testing•5 minutes
  • Posterior probabilities of hypotheses and Bayes factors•6 minutes
  • The Normal-Gamma Conjugate Family•6 minutes
  • Inference via Monte Carlo Sampling•4 minutes
  • Predictive Distributions and Prior Choice•5 minutes
  • Reference Priors•7 minutes
  • Mixtures of Conjugate Priors and MCMC•6 minutes
  • Hypothesis Testing: Normal Mean with Known Variance•8 minutes
  • Comparing Two Paired Means Using Bayes' Factors•6 minutes
  • Comparing Two Independent Means: Hypothesis Testing•4 minutes
  • Comparing Two Independent Means: What to Report?•5 minutes
3 readings•Total 310 minutes
  • Module Learning Objectives•120 minutes
  • Week 3 Lab Instructions (RStudio)•180 minutes
  • Week 3 Lab Instructions (RStudio Cloud)•10 minutes
3 assignments•Total 86 minutes
  • Week 3 Practice Quiz•16 minutes
  • Week 3 Lab•30 minutes
  • Week 3 Quiz•40 minutes

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.

What's included

11 videos3 readings3 assignments

11 videos•Total 72 minutes
  • Bayesian regression•1 minute
  • Bayesian simple linear regression•8 minutes
  • Checking for outliers•4 minutes
  • Bayesian multiple regression•5 minutes
  • Model selection criteria•6 minutes
  • Bayesian model uncertainty•7 minutes
  • Bayesian model averaging•7 minutes
  • Stochastic exploration•8 minutes
  • Priors for Bayesian model uncertainty•9 minutes
  • R demo: crime and punishment•10 minutes
  • Decisions under model uncertainty•8 minutes
3 readings•Total 310 minutes
  • Module Learning Objectives•120 minutes
  • Week 4 Lab Instructions (RStudio Cloud)•180 minutes
  • Week 4 Lab Instructions (RStudio Cloud)•10 minutes
3 assignments•Total 82 minutes
  • Week 4 Practice Quiz•20 minutes
  • Week 4 Lab•22 minutes
  • Week 4 Quiz•40 minutes

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.

What's included

3 videos1 reading

3 videos•Total 23 minutes
  • Bayesian inference: a talk with Jim Berger•9 minutes
  • Bayesian methods and big data: a talk with David Dunson•9 minutes
  • Bayesian methods in biostatistics and public health: a talk with Amy Herring•5 minutes
1 reading•Total 10 minutes
  • About this module•10 minutes

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.

What's included

2 readings1 peer review

2 readings•Total 190 minutes
  • Project information•180 minutes
  • Share your learning experience•10 minutes
1 peer review•Total 60 minutes
  • Data Analysis Project•60 minutes

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Instructors

Instructor ratings
3.6 (56 ratings)
Duke University
11 Courses•431,899 learners
Duke University
2 Courses•78,072 learners
Duke University
2 Courses•78,072 learners

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Showing 3 of 799

MB
·

Reviewed on Oct 25, 2016

Great course with clear instruction and a final peer-review project with clear expectations and explanations.

MC
·

Reviewed on Jun 20, 2018

It was a good course, though I would include more coursework and exercises in R to assist with comprehending a difficult subject. Overall, good course for something that's difficult to teach.

KM
·

Reviewed on Jun 2, 2017

Learnt a lot. Though the subject material was hard to grasp first hand, it is good that instructor was readily available to help us through.

Frequently asked questions

We assume you have knowledge equivalent to the prior courses in this specialization.

No. Completion of a Coursera course does not earn you academic credit from Duke; therefore, Duke is not able to provide you with a university transcript. However, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

Financial aid available,