Bayesian Statistical Concepts and Methods
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Bayesian Statistical Concepts and Methods
This course is part of Modern Statistics for Data-Driven Decision-Making Specialization
Instructors: George Runger
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What you'll learn
Participants will learn fundamentals of Bayesian concepts and methods, including Bayesian models, Bayesian networks, and Markov chain Monte Carlo.
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January 2026
3 assignments
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There are 3 modules in this course
Welcome to Bayesian Statistical Concepts and Methods. In this course, you will use Bayesian methods in data analysis and modeling; work with posterior distributions, distributions without closed form, directed acyclic graphs, Markov Chain Monte Carlo algorithms; and employ R and the Stan platform for statistical modeling. You will also be introduced to Bayesian hierarchical models, which are useful for the interpretation of multi-level data (sub-group versus group).
This Specialization covers the use of statistical methods in today's business, industrial, and social environments, including several new methods and applications. H.G. Wells foresaw an era when the understanding of basic statistics would be as important for citizenship as the ability to read and write. Modern Statistics for Data-Driven Decision-Making teaches the basics of working with and interpreting data, skills necessary to succeed in Wellsβs βnew great complex worldβ that we now inhabit. In this course, learners will be able to use Bayesian methods in data analysis and modeling, to work with posterior distributions, distributions without closed form, directed acyclic graphs, and Markov chain Monte Carlo algorithms, and to use R and the Stan platform for statistical modeling. Learn more about the instructors who developed this course. Read the instructor bios and review the learning outcomes for the course.
What's included
5 videos3 readings1 assignment
5 videosβ’Total 24 minutes
- Course Introductionβ’3 minutes
- Segment 1: Introduction to Bayesian Analysisβ’11 minutes
- Segment 2: Bayesian Estimation of Parameters: Concepts and Mathematical Expressionβ’5 minutes
- Segment 3: Example: Bayes Estimator for the Mean of a Normal Distributionβ’3 minutes
- Segment 4: Conclusions: Bayesian Lessons from the Exampleβ’2 minutes
3 readingsβ’Total 25 minutes
- Course Resources and Peer Reviewsβ’5 minutes
- Instructor Biosβ’10 minutes
- Concepts and Fundamentals of Bayesian Analysis Lecture - Video Segment Overviewβ’10 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Overview of Bayesian Data Analysisβ’30 minutes
In Module 2, we will draw a Bayesian model as a graph and distinguish posterior distribution, posterior predictive distribution, and expected loss or cost. We will also calculate distributions without closed form, recognizing that we can use computational methods to draw from the distribution even when there's no straight-forward equation to define them. Be sure to review the learning objectives before beginning work in this module.
What's included
9 videos2 readings1 assignment
9 videosβ’Total 34 minutes
- Segment 1: Working with Bayesian Models: Conventionsβ’2 minutes
- Segment 2: Example, Part A: Silicon Wafer Cleaning - Priors and Posteriorsβ’5 minutes
- Segment 3: Example, Part B: Silicon Wafer Cleaning - Wafer Thickness Prediction (Fixed Mean) and Decisionβ’3 minutes
- Segment 4: Example, Part C: Silicon Wafer Cleaning - Wafer Thickness Prediction and Decision (Uncertain Mean and Variance) Using Stan Modelβ’4 minutes
- Segment 5: Working with Bayesian Models: Summaryβ’1 minute
- Segment 1: Introduction to Bayesian Networks and Covid Testing Exampleβ’7 minutes
- Segment 2: Cancer Diagnosis: Building and Querying a Bayesian Network Using Rβ’8 minutes
- Segment 3: Advanced Queries and Evidence Updates in Bayesian Networksβ’2 minutes
- Segment 4: Applications and Information Value, Parameter Fitting, and Extensionsβ’3 minutes
2 readingsβ’Total 20 minutes
- Bayesian Models and Posterior Distributions Lecture - Video Segment Overviewβ’10 minutes
- Bayesian Networks Lecture - Video Segment Overviewβ’10 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Bayesian Simulation and Estimationβ’30 minutes
In Module 3, we will employ R and the Stan platform for statistical modeling. You will explore Bayesian methods in data analysis and modeling; work with posterior distributions, distributions without closed form, directed acyclic graphs, and Markov Chain Monte Carlo algorithms. You will also be introduced to Bayesian hierarchical models, which estimate subgroup parameters relative to the parameters of a larger parent group. Be sure to view the course introduction video and review the learning objectives before beginning work in this module.
What's included
10 videos3 readings1 assignment1 peer review
10 videosβ’Total 48 minutes
- Segment 1: Using Stan Function in R to Assemble Bayesian or Other Modelsβ’3 minutes
- Segment 2: Stan Model Definition and Syntaxβ’3 minutes
- Segment 3: Stan Sampling and Posterior Analysisβ’8 minutes
- Segment 4: Advanced Stan Modeling: Bayesian Fitβ’2 minutes
- Segment 5: Optimization and Simulation Studies in Stanβ’4 minutes
- Segment 1: Diagnosing Stan Output: Common Diagnostic Issues and Metricsβ’3 minutes
- Segment 2: The "Eight Schools" Case Example: Applied Diagnostics and Plots Reveal Problemsβ’8 minutes
- Segment 3: Understanding Stan Divergences and Errors: Advanced Diagnostic Tools and Strategiesβ’4 minutes
- Segment 4: Reparameterization and Model Improvementβ’3 minutes
- Partial Poolingβ’9 minutes
3 readingsβ’Total 30 minutes
- Modeling Using Stan Lecture - Video Segment Overviewβ’10 minutes
- Stan Diagnostics Lecture - Video Segment Overviewβ’10 minutes
- Stan Resourcesβ’10 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Modeling Using Stanβ’30 minutes
1 peer reviewβ’Total 60 minutes
- Mini-Project for Modern Statistics for Data-Driven Decision-Makingβ’60 minutes
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