Overview

The course "Bayesian Hierarchical Modelling" provides an introduction to the formulation, fitting and checking of hierarchical or multilevel models from the Bayesian point of view. Hierarchical models (HMs) arise frequently in three main kinds of applications:

1. HMs are common in fields such as health and education, in which data---both outcomes and predictors---are often gathered in a nested or hierarchical fashion, e.g., patients within hospitals, or students within classrooms within schools. HMs are thus also ideally suited to the wide range of applications in government and business in which single- or multi-state cluster samples are routinely drawn, and offer a unified approach to the analysis of random-effects (variance-components) and mixed models.
2. A different kind of nested data comes up in meta-analysis in, e.g., medicine and the social sciences. In this setting, the goal is combining information from a number of studies of essentially the same phenomenon, to produce more accurate inferences and predictions than those available from any single study. Here the data structure is subjects within studies, and as in the clustered case above there will generally be predictors available at both the subject and study levels; and
3. Hierarchical modelling also provides a natural way to treat issues of model selection and model uncertainty with all types of data, not just cluster samples. For example, in regression if the data appear to exhibit residual variation that changes with the predictors, you can expand the model that assumes constant variation, by embedding it in a family of models that span a variety of assumptions about residual variation. In this way, instead of having to choose one of these models and risk making the wrong choice, you can work with several models at once, weighting them in proportion to their plausibility given the data.

The Bayesian approach is particularly effective in fitting hierarchical models, because other model-based methods---based principally on maximum likelihood---often do not capture all relevant sources of uncertainty, leading to over-confident decisions and scientific conclusions.

In this course the principles of Bayesian hierarchical modelling are described with emphasis on practical rather than theoretical issues, and illustrated with real data drawn from case studies. The course is intended for applied statisticians with an interest in learning more about hierarchical models in general, and the Bayesian analysis of such models in particular. An understanding of probability at the level typically required for a master's degree in statistics provides sufficient mathematical background. No previous experience with Bayesian methods is needed---all relevant ideas are covered in the course in a self-contained fashion.

Objectives

Participants will learn how to translate scientific and decision-making problems involving nested or clustered data into appropriate hierarchical models (including random-effects and mixed models), and will also learn how---with any kind of data, not just a cluster sample---to embed a given model hierarchically in a richer model class, as a way to realistically approach issues of model selection and model uncertainty. Participants will learn methods for computing posterior and predictive distributions for quantities of interest arising in the hierarchical models and to examine the results of the model-fitting for weaknesses and for sensitivity to modelling assumptions.

I will meet these objectives by exploring three case studies---from education, health policy, and engineering risk assessment---with emphasis on the practical interaction between scientific, decision-making, and statistical considerations. Several other real examples will also be used to illustrate particular concepts. Software details required for carrying out the analyses will be provided in the course materials.

Target Population

The principal target audience includes applied statisticians (1) who work with clustered data on a regular basis, or are about to begin doing so; (2) who wish to gain experience in the modern fitting of random-effects and mixed models, in meta-analysis and other settings; and (3) who wish to learn about current methods for coping with problems of model selection and model uncertainty (with all kinds of data, not just cluster samples). Application areas in which hierarchical modelling occurs frequently include policy analysis and other governmental activities, agriculture, medicine and health, education, and biology. Others who may be interested in this course include applied and methodological workers who wish to learn more about (4) comparisons in complexity and performance between Bayesian and frequentist methods, and (5) Markov Chain Monte Carlo techniques and how to ensure that they work well in practice. There are no formal mathematical prerequisites, but a working knowledge of probability at the master's level (from such books as Hogg and Craig, Bickel and Doksum or Casella and Berger)---particularly the ability to conceptualize and manipulate conditional probabilities---will be helpful.

Learning Outcomes

Participants will develop and/or extend facility in: Formulating appropriate hierarchical (random-effect and/or mixed) models for clustered outcomes in meta-analyses and other studies, both qualitative and quantitative, and in situations with predictor information available at some or all levels of the hierarchy; using Bayesian reasoning and Markov Chain Monte Carlo methods to compute posterior distributions for parameters of greatest interest in a given hierarchical model; diagnosing problems with a given hierarchical model by looking for discrepancies between predictive distributions for observables and the actual values the observables take on; and hierarchically expanding an existing model (for all kinds of data, not just cluster samples) which does not pass all diagnostic checks, by embedding it in a richer model class of which it is a special case.

Biography

David Draper is a Professor of Statistics in the School of Mathematical Sciences at the University of Bath in England. David did his Ph.D. work at the University of California, Berkley, finishing in 1981 and has since taught and done consulting and public policy research at the University of Chicago (1981-84), the RAND Corporation (1984-91), UCLA (1991-93), the University of Bath (1993-Present), with a sabbatical visit to the University of Washington in 1986. He is a fellow of the Royal Statistical Society and a member of both the IMSV and ASA. David has served as Associate Editor for the Journal of the American Statistical Association and the Journal of the Royal Statistical Society, and is the author or coauthor of four books and 46 articles and other substantial contributions to refereed journals.

David has been nominated for teaching awards at every university in which he has taught and was the recipient of the Quntrell Award of Excellence in Undergraduate Teaching at the University of Chicago. He was also the recipient of an Excellence in Continuing Education award for his course offerings at the Anaheim and Dallas Joint Statistical Meetings through the Continuing Education Program.

Registration Price:
$375 Interface Participants and ASA Members
$475 Non-Interface Participants and Non-ASA Members
$200 Full-time Students

Registration Code:
3530-2004-01