Introduction to Bayesian Hierarchical and Multi-level Models

Introduction to Bayesian Hierarchical and Multi-level Models

taught by Peter Congdon

Aim of Course:

This online course, "Introduction to Bayesian Hierarchical and Multi-level Models" extends the Bayesian modeling framework to cover hierarchical models, and to add flexibility to standard Bayesian modeling problems.  Participants will learn how to define three-stage hierarchical models and to implement them using Winbugs, in multilevel, meta-analytic and regression applications.  Continuous, count and binary outcomes are covered.  Participants will also learn how to assess goodness-of-fit.

This course may be taken individually (one-off) or as part of a certificate program.
Course Program:

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 Multilevel 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


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.

Introduction to Bayesian Hierarchical and Multi-level Models

Who Should Take This Course:
Statistical analysts with some familiarity with Bayesian analysis who want to deepen their skill set in Bayesian modeling.
Students should also have some familiarity with BUGS software (WinBUGS/OPENBUGS).
Organization of the Course:

This course has an end of course modeling project and provides example software codes.

Options for Credit and Recognition:

Specializations are an easy way for you to demonstrate mastery of a specific skill in statistics and analytics. This course is part of the Bayesian Statistics Specialization which uses Bayes' Theorem to perform analyses and computations, and learn what makes it so popular.

Course Text:

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

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


May 17, 2019 to June 14, 2019 May 15, 2020 to June 12, 2020

Introduction to Bayesian Hierarchical and Multi-level Models


May 17, 2019 to June 14, 2019 May 15, 2020 to June 12, 2020

Course Fee: $589

Do you meet course prerequisites? What about book & software? (Click here to learn more)

We have flexible policies to transfer to another course, or withdraw if necessary (modest fee applies)

Group rates: Click here to get information on group rates. 

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