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Introduction to Bayesian Hierarchical and Multi-level Models

Introduction to Bayesian Hierarchical and Multi-level Models

This course will teach you how to extend the Bayesian modeling framework to cover hierarchical models and to add flexibility to standard Bayesian modeling problems.


Complex sample designs such as stratified cluster sampling make it possible to extract maximum information at minimum cost, but they are typically harder to work with than simple random samples. How do you analyze the resulting data – in particular, how do you determine margins of error? This course teaches you how to estimate variances when analyzing survey data from complex samples, and also how to fit linear and logistic regression models to complex sample survey data.

  • Intermediate, Advanced
  • 4 Weeks
  • Expert Instructor
  • Tuiton-Back Guarantee
  • 100% Online
  • TA Support

Learning Outcomes

Students who complete this course will learn how to define Bayesian hierarchical models, hierarchical models for meta analysis, and hierarchical Bayesian regression models. They will explore computing options (BUGS and R) and Winbugs implementation for various Bayesian analyses.

  • Specify 3-stage Bayesian hierarchical model
  • Measure model fit and check parameters
  • Model the variance/covariance in Bayesian random effects models
  • Apply Bayesian hierarchical models to meta-analysis
  • Specify multi-level and panel models
  • Manage overdispersion for count and proportion data

Who Should Take This Course

Statistical analysts with some familiarity with Bayesian analysis who want to deepen their skill set in Bayesian modeling.

Our Instructors

Dr. Peter Congdon

Dr. Peter Congdon

Dr. Peter Congdon is a Research Professor in Quantitative Geography and Health Statistics at Queen Mary University of London. He is the author of several books and numerous articles in peer-reviewed journals. His research interests include spatial data analysis, Bayesian statistics, latent variable models, and epidemiology.

Course Syllabus

Week 1

Defining Bayesian Hierarchical Models

  • Overview of application contexts: meta-analysis to summarise accumulated evidence; comparisons of related units (e.g. “league table comparisons” of exam results, hospital mortality rates, etc); rationale for multi-level models in health, education etc
  • Defining Hierarchical Bayesian Models. Three stage models.
  • Benefits from “borrowing strength” using Bayesian random effect models.
  • Measuring model fit for hierarchical models, and procedures for model checking; effective parameters (and DIC)
  • Common conjugate hierarchical models with worked examples
  • Computing options (BUGS and R)

Week 2

Bayesian Hierarchical Models for Meta Analysis

  • Modelling the variance/covariance in Bayesian random effects models. Alternative priors for variances. Winbugs implementation of these priors.
  • Bayesian meta-analysis and pooled estimates in clinical studies and education
  • Different meta-analysis schemes (e.g. beta-binomial, logit-normal for binomial data)

Week 3

Multi-Level and Panel Models

  • Multi-level models (2 and 3 level models for continuous, count and binary responses) and Winbugs implementation to include data input structures.
  • Simple panel models (random intercept, random slope) from a Bayesian perspective.

Week 4

More on Multi-level Models; Hierarchical Bayesian Regression Models

  • Crossed and multivariate and multilevel models
  • Overdispersed regression options for count and proportion data including negative binomial and beta-binomial regression


Students should also have some familiarity with WinBUGS/OPENBUGS software.

Introduction to Bayesian Computing and Techniques

This course will teach you how to apply Markov Chain Monte Carlo techniques (MCMC) to Bayesian statistical modeling using WinBUGS software.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Introduction to R Programming

This course provides an easy introduction to programming in R.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Class Dates


11/25/2022 to 12/23/2022


11/24/2023 to 12/22/2023


11/22/2024 to 12/20/2024
Karolis Urbonas
Susan Kamp
Stephen McAllister
Amir Aminimanizani
Elena Rose
Leonardo Nagata
Richard Jackson

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Introduction to Bayesian Hierarchical and Multi-level Models

Additional Information


Homework in this course consists of short answer questions to test concepts, guided data analysis and modeling problems using software.

In addition to assigned readings, this course also has end of course data modeling project, and example software codes.

Course Text

Recommended Reading:  Congdon, P (2003) Applied Bayesian Modelling


The course will be based on the freeware BUGS package (WinBUGS/OPENBUGS).

Supplemental Information

Literacy, Accessibility, and Dyslexia

At, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:







  • Navidys (for colorblindness, dyslexia, and reading difficulties)
  • HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

Register For This Course

Introduction to Bayesian Hierarchical and Multi-level Models