Applied Mathematics & Statistics (AMS)
Reading 2017, Days 1 and 2: Bayesian Modeling, Inference, Prediction and Decision-Making
Topics will include a review of classical, frequentist, and Bayesian definitions of probability; sequential learning via Bayes' Theorem; coherence as a form of internal calibration; Bayesian decision theory via maximization of expected utility; review of frequentist modeling and maximum-likelihood inference; exchangeability as a Bayesian concept parallel to frequentist independence; prior, posterior, and predictive distributions; Bayesian conjugate analysis of binary outcomes, and comparison with frequentist modeling; integer-valued outcomes (Poisson modeling); continuous outcomes (Gaussian modeling); multivariate unknowns and marginal posterior distributions; introduction to simulation-based computation, including rejection sampling and Markov chain Monte Carlo (MCMC) methods; and MCMC implementation strategies.
The case studies will be drawn from medicine (diagnostic screening for HIV; hospital-specific prediction of patient-level mortality rates; hospital length of stay for premature births) and the physical sciences (measurement of physical constants), but the methods illustrated will apply to a broad range of subject areas in the natural and social sciences, business (including topics of direct relevance to pharmaceutical companies), and public policy.
Through a series of practicals (computer labs), the course will liberally illustrate (a) the use of the freeware statistical computing environment R for Bayesian closed-form computations and (b) user-friendly implementations of MCMC sampling via the freeware programs WinBUGS (for Windows platforms) and rjags (for all platforms) when closed-form solutions are not possible.
The course is intended mainly for people who often use statistics in their research; some graduate coursework in statistics will provide sufficient mathematical background for participants. To get the most out of the course, participants should be comfortable with hearing the course presenter mention (at least briefly) (a) differentiation and integration of functions of several variables and (b) discrete and continuous probability distributions (joint, marginal, and conditional) for several variables at a time, but all necessary concepts will be approached in a sufficiently intuitive manner that rustiness on these topics will not prevent understanding of the key ideas.
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 145 contributions to the methodological and applied statistical literature, including articles in the Journal of the Royal Statistical Society (Series A, B and C), 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 about 1,650 times, and taken together his publications have been cited about 14,500 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, environmental risk assessment and data science.
His short courses have received Excellence in Continuing Education Awards from the American Statistical Association on two occasions. 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.
(last modified: 16 November 2017)