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Bayesian Statistics

Approx. 35 hours to complete

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Course Summary

Learn Bayesian statistics and inference from scratch with the Bayesian Statistics course on Coursera. This course teaches you how to make probabilistic statements with confidence, and how to use Bayes' theorem to solve complex problems.

Key Learning Points

Understand the basic principles of Bayesian inference
Learn how to use Bayes' theorem to solve problems
Apply Bayesian methods to real-world scenarios

Learning Outcomes

Ability to understand and apply Bayesian statistical inference
Ability to use Bayes' theorem to solve complex problems
Ability to apply Bayesian methods to real-world scenarios

Prerequisites or good to have knowledge before taking this course

Basic understanding of probability theory
Familiarity with basic statistical concepts

Course Difficulty Level

Intermediate

Course Format

Online
Self-paced

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Notable People in This Field

Professor of Statistics and Political Science
Professor of Public Understanding of Risk
Science Writer

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Description

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.

Outline

About the Specialization and the Course
Introduction to Statistics with R
About Statistics with R Specialization
About Bayesian Statistics
Pre-requisite Knowledge
Special Thanks

The Basics of Bayesian Statistics
The Basics of Bayesian Statistics
Conditional Probabilities and Bayes' Rule
Bayes' Rule and Diagnostic Testing
Bayes Updating
Bayesian vs. frequentist definitions of probability
Inference for a Proportion: Frequentist Approach
Inference for a Proportion: Bayesian Approach
Effect of Sample Size on the Posterior
Frequentist vs. Bayesian Inference
Module Learning Objectives
About Lab Choices
Week 1 Lab Instructions (RStudio)
Week 1 Lab Instructions (RStudio Cloud)
Week 1 Lab
Week 1 Practice Quiz
Week 1 Quiz

Bayesian Inference
Bayesian Inference
From the Discrete to the Continuous
Elicitation
Conjugacy
Inference on a Binomial Proportion
The Gamma-Poisson Conjugate Families
The Normal-Normal Conjugate Families
Non-Conjugate Priors
Credible Intervals
Predictive Inference
Module Learning Objectives
Week 2 Lab Instructions (RStudio)
Week 1 Lab Instructions (RStudio Cloud)
Week 2 Lab
Week 2 Practice Quiz
Week 2 Quiz

Decision Making
Decision making
Losses and decision making
Working with loss functions
Minimizing expected loss for hypothesis testing
Posterior probabilities of hypotheses and Bayes factors
The Normal-Gamma Conjugate Family
Inference via Monte Carlo Sampling
Predictive Distributions and Prior Choice
Reference Priors
Mixtures of Conjugate Priors and MCMC
Hypothesis Testing: Normal Mean with Known Variance
Comparing Two Paired Means Using Bayes' Factors
Comparing Two Independent Means: Hypothesis Testing
Comparing Two Independent Means: What to Report?
Module Learning Objectives
Week 3 Lab Instructions (RStudio)
Week 3 Lab Instructions (RStudio Cloud)
Week 3 Lab
Week 3 Practice Quiz
Week 3 Quiz

Bayesian Regression
Bayesian regression
Bayesian simple linear regression
Checking for outliers
Bayesian multiple regression
Model selection criteria
Bayesian model uncertainty
Bayesian model averaging
Stochastic exploration
Priors for Bayesian model uncertainty
R demo: crime and punishment
Decisions under model uncertainty
Module Learning Objectives
Week 4 Lab Instructions (RStudio Cloud)
Week 4 Lab Instructions (RStudio Cloud)
Week 4 Lab
Week 4 Practice Quiz
Week 4 Quiz

Perspectives on Bayesian Applications
Bayesian inference: a talk with Jim Berger
Bayesian methods and big data: a talk with David Dunson
Bayesian methods in biostatistics and public health: a talk with Amy Herring
About this module

Data Analysis Project
Project information

Summary of User Reviews

Discover the power of Bayesian statistics with this comprehensive course on Coursera. Users have rated this course highly for its engaging content and practical applications in real-world scenarios.

Key Aspect Users Liked About This Course

Many users appreciated the practical applications of Bayesian statistics taught in this course.

Pros from User Reviews

Engaging content that keeps learners interested throughout the course
Real-world examples and applications make the material easy to understand
Great instructor who explains complex concepts in a clear and concise manner

Cons from User Reviews

Some users found the material to be too advanced for beginners
The pace of the course is quite fast, which can be difficult for some learners to keep up with
The course could benefit from more interactive elements and hands-on activities

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