Bayesian hierarchical/multilevel and latent-variable (random-effects) modeling A short course presented by David Draper Department of Applied Mathematics and Statistics University of California, Santa Cruz, USA National University of Ireland, Galway Abstract This half-day short course will cover a variety of methodological topics and examples in Bayesian hierarchical/multilevel and latent-variable (random-effects) modeling. With the advent of Markov-Chain Monte Carlo (MCMC) algorithms for sampling from posterior distributions, these powerful models have become increasingly practical, and they are now routinely being used to answer important scientific questions in many fields, including education, health policy, and medicine. Multilevel data sets (cluster samples) with a nested character --- for example, patients nested in hospitals, or students nested in classrooms nested in schools --- and covariates at all levels are ubiquitous in the social and medical sciences; when such data sets include random samples at several levels of the hierarchy, random-effects models are natural. Even with data not possessing a multilevel character, latent-variable random effects can be helpful in describing unexplained heterogeneity, so that well-calibrated uncertainty assessments are possible. In this short course the following topics will be covered: * Formulation of Bayesian models and fitting them via MCMC with WinBUGS. * Fixed- and random-effects models in meta-analysis; case studies: effects of aspirin on mortality for heart attack patients, effects of teacher expectancy on student performance. * Fixed- and random-effects additive, multiplicative and hierarchical regression models for count data; case study: effects of in-home geriatric assessment on hospitalization rates for elderly people living in the community. * Random-effects logistic regression models for multilevel data sets with binary outcomes; case study: effects of socio-economic and other variables on type of prenatal care for Guatemalan women. * Bayesian hierarchical modeling as an alternative to variable selection in generalized linear models; case study: prediction of body fat in humans. About the instructor David Draper is a Professor of Statistics in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (USA). He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association (ASA), the Institute of Mathematical Statistics, and the Royal Statistical Society; from 2001 to 2003 he served as the President-Elect, President, and Past President of the International Society for Bayesian Analysis (ISBA). He is the author or co-author of about 100 contributions to the methodological and applied statistical literature, including articles in the Journal of the Royal Statistical Society (Series A and B), the Journal of the American Statistical Association, the Annals of Applied Statistics, Bayesian Analysis, Statistical Science, the New England Journal of Medicine, and the Journal of the American Medical Association; his 1995 JRSS-B article on assessment and propagation of model uncertainty has been cited more than 850 times. His research is in the areas of Bayesian inference and prediction, model uncertainty and empirical model-building, hierarchical modeling, Markov Chain Monte Carlo methods, and Bayesian nonparametric methods, with applications mainly in medicine, health policy, education, and environmental risk assessment. When he gave a longer version of this short course at the Anaheim Joint Statistical Meetings (JSM) in 1997 it received the 1998 ASA Excellence in Continuing Education award, and a short course he gave on intermediate and advanced-level topics in Bayesian hierarchical modeling at the San Francisco JSM in 2003 received the 2004 ASA Excellence in Continuing Education award. He has won or been nominated for major teaching awards everywhere he has taught (the University of Chicago; the RAND Graduate School of Public Policy Studies; the University of California, Los Angeles; the University of Bath (UK); and the University of California, Santa Cruz). He has a particular interest in the exposition of complex statistical methods and ideas in the context of real-world applications.