Dates: May 15-19, 2006
Location: American University
Objectives and Scope
Bayesian analysis provides a unified and coherent way of thinking about decision problems and their solution using data and other information. The goal of this course is to acquaint the student in a serious way with this approach and its problem solving potential, and to this end it has two objectives. The first is to provide a clear understanding of Bayesian analysis, grounded in the theory of inference and optimal decision making, which will enable the student to confidently analyze real problems. The second is to equip the student with state-of-the-art simulation methods that can be used to solve these problems.
The course begins with an overview of the entire topic, including decision problems that motivate Bayesian analysis, principles of conditioning, updating and combining information, and using modern computer simulation methods to provide a smooth interface between data, inference and decision-making. We will work a few common problems with uncommon solutions to cement the difference between Bayesian and non-Bayesian inference.
After spending an afternoon on the essential theory of Bayesian econometrics, the course moves into the computer simulation methods that revolutionized the entire approach to Bayesian analysis beginning in the late 1980’s. The course will provide both analytical understanding of these methods and hands-on experience with how they work (and when they won’t). We will apply these methods not just to “estimation” as conventionally defined, but also to the solution of some realistic decision-making problems.
The course continues by introducing some of the key innovations that have made Bayesian analysis a flexible and realistic tool for modeling and decision-making. The emphasis in these innovations is on methods that are both theoretically sound and also provide practical approaches of demonstrated superiority in decision making. The course will also convey some of the “oral wisdom” of practitioners in developing computer code that is reliable and runs fast enough to get the job done.
The course will conclude with the presentation of some of the instructor’s recent experience in forecasting and financial decision making, and with the opportunity for students to put forward current problems in research and decision making and see how they might be addressed by contemporary methods of Bayesian analysis.
Content and topics (Reference is to chapters and sections in the required text.)
Monday, May 15 (morning) Chapter 1
Review and overview of Bayesian methods (1.1-1.6)
Learning session (Selected exercises, ch. 1)
Monday, May 15 (afternoon) Sections 2.1-2.3
Bayesian inference in the linear model (2.1)
Sufficiency and conjugate prior distributions (2.2-2.3)
Tuesday, May 16 (morning) Sections 4.1-4.3
Posterior simulation methods using i.i.d. simulation (4.1-4.2)
Markov chain Monte Carlo methods (4.3)
Tuesday, May 16 (afternoon)
Computer lab session: BACC and the linear model (5.1)
Bayesian decision theory and the combination of information (2.4-2.6)
Wednesday, May 17 (morning)
Computer lab session: Decision making with the linear model (Selected exercises, 5.1)
Hierarchical priors, latent variables and discrete choice (3.1, 6.1, 6.2)
Thursday, May 18 (morning)
Flexible models (5.4, 6.4.2)
Computer lab session: Using flexible models (Exercises, 5.4 and/or 6.4)
Thursday, May 18 (afternoon)
Tricks of the trade I: Making sure it works (8.1, 8.3)
Tricks of the trade II: Making it work faster (4.4, 4.6)
Friday, May 19 (morning)
Model comparison and Bayesian communication (8.2, 8.4)
Smoothly mixing regressions (Working paper)
Friday, May 19 (afternoon)
Open session: Topics as dictated by student interests and current concerns in research or decision-making support.
Computer lab session and “hands on” work
The class will move fairly freely between theory, data and simulation methods for Bayesian inference. The course will emphasize Matlab in conjunction with the Bayesian Analysis, Computation and Communications (BACC) software in much of our work, but prior knowledge of MATLAB will not be assumed.
Target group and requirements
This course will be of interest to students who have completed a year of econometrics at the Ph.D. level, and to professional economists and econometricians who work in support of decision making in any setting, including mission-oriented government agencies and private consulting firms. Participants should have some prior experience using a mathematical applications software package (e.g. Matlab, Gauss, R, …).
The course can be taken for three credits or for no credit. To receive the full three credits, the participant needs to complete a research paper. Credits can only be obtained by writing the applied paper. Students can start working on the paper at the end of the course. The paper is due a number of weeks after the end of the sessions.
The course will use the text Contemporary Bayesian Econometrics and Statistics (Wiley, 2005), written by the instructor. Students should purchase a copy of this text before the course begins. One of the sessions will also use the paper “Smoothly Mixing Regressions” (Journal of Econometrics, forthcoming) by Geweke and Keane (see link below).
John Geweke is a widely-known academic econometrician who has made important contributions to time series analysis and Bayesian econometrics, and has applied these methods in many areas of economics. He is an elected fellow of the Econometric Society and the American Statistical Association, co-editor of the Journal of Econometrics, and is a past member of the Committee on National Statistics of the National Academy of Sciences. He has provided econometric support for decision making as a consultant to several government agencies and to firms in the private sector