Bayesian Statistics

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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 …

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

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, Assistant 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 3.8 stars Average User Rating 3.8See what learners said Coursework

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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 expand


  1. Video: Introduction to Statistics with R
  2. Reading: About Statistics with R Specialization
  3. Reading: About Bayesian Statistics
  4. Reading: Special Thanks
  5. Reading: Weekly Feedback Forms
  6. 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 expand


  1. Video: The Basics of Bayesian Statistics
  2. Reading: Module Learning Objectives
  3. Video: Conditional Probabilities and Bayes' Rule
  4. Video: Bayes' Rule and Diagnostic Testing
  5. Video: Bayes Updating
  6. Video: Bayesian vs. frequentist definitions of probability
  7. Video: Inference for a Proportion: Frequentist Approach
  8. Video: Inference for a Proportion: Bayesian Approach
  9. Video: Effect of Sample Size on the Posterior
  10. Video: Frequentist vs. Bayesian Inference
  11. Practice Quiz: Week 1 Practice Quiz
  12. Reading: Week 1 Lab Instructions
  13. 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 expand


  1. Video: Bayesian Inference
  2. Reading: Module Learning Objectives
  3. Video: From the Discrete to the Continuous
  4. Video: Elicitation
  5. Video: Conjugacy
  6. Video: Inference on a Binomial Proportion
  7. Video: The Gamma-Poisson Conjugate Families
  8. Video: The Normal-Normal Conjugate Families
  9. Video: Non-Conjugate Priors
  10. Video: Credible Intervals
  11. Video: Predictive Inference
  12. Practice Quiz: Week 2 Practice Quiz
  13. Reading: Week 2 Lab Instructions
  14. 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 expand


  1. Video: Decision making
  2. Reading: Module Learning Objectives
  3. Video: Losses and decision making
  4. Video: Working with loss functions
  5. Video: Minimizing expected loss for hypothesis testing
  6. Video: Posterior probabilities of hypotheses and Bayes factors
  7. Video: Comparing two proportions using Bayes factors: assumptions
  8. Video: Comparing two proportions using Bayes factors
  9. Video: Comparing two paired means using Bayes factors
  10. Video: What to report?
  11. Video: Posterior probability, p-values and paradoxes
  12. Video: Comparing two independent means
  13. Video: Comparing two independent means: hypothesis testing
  14. Practice Quiz: Week 3 Practice Quiz
  15. Reading: Week 3 Lab Instructions
  16. 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 expand


  1. Video: Bayesian regression
  2. Reading: Module Learning Objectives
  3. Video: Bayesian simple linear regression
  4. Video: Checking for outliers
  5. Video: Bayesian multiple regression
  6. Video: Model selection criteria
  7. Video: Bayesian model uncertainty
  8. Video: Bayesian model averaging
  9. Video: Stochastic exploration
  10. Video: Priors for Bayesian model uncertainty
  11. Video: R demo: crime and punishment
  12. Video: Decisions under model uncertainty
  13. Practice Quiz: Week 4 Practice Quiz
  14. Reading: Week 4 Lab Instructions
  15. Reading: Week 4 Lab Supplement
  16. 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.


5 videos, 1 reading expand


  1. Video: Perspectives on Bayesian applications
  2. Video: Bayesian inference: a talk with Jim Berger
  3. Video: Bayesian methods and big data: a talk with David Dunson
  4. Video: Bayesian methods in biostatistics and public health: a talk with Amy Herring
  5. Video: Bayes in industry: a talk with Steve Scott
  6. 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 expand


  1. Reading: Project information
  2. Reading: Weekly Feedback Form

Graded: Data Analysis Project
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