商务统计与经济计量系短期课程
Title（题目）：Monte Carlo Methods in Bayesian Computation
Speaker（报告人）：Prof.Minghui Chen, The University of Connecticut
Time（时间）：2012年7月11日（周三）上午09:00-11:00，下午2:00-4:00
Place（地点）：北京大学光华管理学院新楼217教室
Abstract（摘要）：As is well-known, in advanced Bayesian computation, there are two major challenges. These are i) how to sample from posterior distributions and ii) how to compute posterior quantities of interest using MCMC samples. These are two equally important aspects in Bayesian computation. In this short course, we will present updates on how to efficiently sample from posterior distributions and discusses how to compute posterior quantities of interest using MCMC samples. Several topics are covered, including basic techniques for random number generation, MCMC sampling, Monte Carlo methods for estimation of posterior expectations, improving simulation accuracy, marginal posterior density estimation, highest posterior density (HPD) interval calculations, Bayes factors, and Bayesian methods for checking model adequacy and related computational techniques.
About the speaker（报告人介绍）：
Ming-Hui Chen, Ph.D. is Professor in the Department of Statistics, University of Connecticut. He received his Ph.D. in Statistics, Purdue University (1993). He was elected to Fellow of the Institute of Mathematical Statistics in 2007, Fellow of American Statistical Association in 2005, an elected ordinary member of the International Statistical Institute (ISI) in 1999. He has been awarded several US NIH and NSF grants since 1994. He co-authored three books: Bayesian Survival Analysis (with J. Ibrahim, D. Sinha), Springer, 2001; Monte Carlo Methods in Bayesian Computation (with Q. Shao, J. Ibrahim), Springer, 2000; and Applied Statistics for Engineers (with J. Petruccelli, B. Nandram), Prentice-Hall, 1999. He also co-edited a book: Frontiers of Statistical Decision Making and Bayesian Analysis --- In Honor of James O. Berger (with Dey, D.K., Müller, P., Sun, D., and Ye, K.), Springer, 2010.He has published over 250 articles in mainstream statistics, biostatistics, and medical journals, including Annals of Statistics, Journal of the American Statistical Association, Biometrika, Journal of the Royal Statistical Society, Series B, C, and D, Biometrics, New England Journal of Medicine, The Lancet, The Journal of the American Medical Association, etc. He serves as an Editor for Bayesian Analysis and Associate Editors for Journal of the American Statistical Association, Lifetime Data Analysis, Sankhya, Series A and B, Journal of Computational and Graphical Statistics, and Statistics and Its Interface. Since 2008, he has been serving as the Director of the Statistical Consulting Services (a statistical consulting center) in the Department of Statistics, University of Connecticut. Currently, he is President-Elect (President, 2013) of the International Chinese Statistical Association (ICSA,) and an elected board member of the International Society for Bayesian Analysis (ISBA).
Dr. Chen has special interest in the areas of Bayesian Statistical Methodology, Categorical Data Analysis, Design of Bayesian clinical trials, Bayesian DNA Microarray Data Analysis, Bayesian Phylogenetics, Meta analysis, Missing Data Analysis (EM, MCEM, and Bayesian), Monte Carlo Methodology, Prior Elicitation, Statistical Analysis and Methodology for Prostate Cancer Data, Statistical Modeling and computing, Survival data analysis, and Variable Selection.
Outline of Short Course
Session 1: Monte Carlo Simulation and MCMC Sampling
9:00am-11:00am
In this session, we will briefly introduce the general setting of computing posterior summaries for data analysis and motivate the idea of Monte Carlo methods. A brief overview of commonly used random number generation techniques and MCMC sampling algorithms will be given and several computational tools to improve convergence of MCMC sampling will be presented and discussed. In addition, several examples will be used to illustrate the computational techniques.
Session 2: Monte Carlo Methods for Estimating Posterior Quantities
2:00pm-4:00pm
In this session, we first introduce some basic Monte Carlo methods including the computation of simulation standard errors, dependent sample versus independent sample, and effect of ``burn in". We then discuss how to estimate posterior marginal density, Bayesian credible intervals, highest probability density (HPD) intervals, and Bayes factors. In addition, we will introduce various Bayesian methods for checking model adequacy and related computational techniques, including Monte Carlo estimation of conditional predictive ordinates (CPO) and various Bayesian residuals.
