### Bayesian Hierarchical 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:

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.

Level:

advanced/intermediate

Students should also have some familiarity with WINBUGS software.

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

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

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

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

Software:

WINBUGS is used in the course; students should have some familiarity with it prior to taking the course (this can be gained in The Institute's other courses on Bayesian analysis).

# Introduction to Bayesian Hierarchical and Multi-level Models

May 19, 2017 to June 16, 2017May 18, 2018 to June 15, 2018