Bayesian Methods in Theory and Practice

Bayesian Methods in Theory and Practice

PhD-course, Mansholt Graduate School

WAGENINGEN UNIVERSITY

by John Geweke

June 19-27, 2006

Introduction:

This course provides an introduction to the use of Bayesian methods in the context of economics and econometrics. However, the set-up of the course also makes it interesting for scientists of other disciplines using Bayesian techniques. In economic theory Bayesian methods are central to modeling behavior under uncertainty. Economic agents typically maximize an objective function conditional on their available information, and as more information becomes available they update their decisions using Bayes rule. Bayesian methods in econometrics apply this paradigm to the economist as an investigator and decision maker: he or she conditions on observed behavior, and then draws inferences about alternative models for behavior or reaches a decision such as a policy recommendation or a forecast. The first day of the course will review the theory of Bayesian inference, including posterior conditioning, sufficiency and ancillarity, credible sets, prior distributions, model comparison, predictive distributions, hierarchical priors, and the likelihood principle.

Until the 1980’s, the potential for the application of Bayesian methods in econometrics was limited by technical demands placed on the investigator. Over the past fifteen years these limitations have been substantially reduced by innovations in scientific computing and drastic drops in the cost of computing. The developments in scientific computing include Monte Carlo methods for the representation of intractable analytical expressions of an investigator’s or an economic agent’s uncertainty. The second and third day of the course will provide the background in these methods needed for an applied econometrician to begin using them. The topics covered in the remaining days will include principles of simulation, importance sampling, and Markov chain Monte Carlo methods, with applications to linear and Markov chain models. There will also be an introduction to the Bayesian Analysis, Computation and Communication (BACC) software that makes these procedures user-friendly.

The Bayesian approach to econometrics, when coupled with Monte Carlo methods for representing uncertainty, expands the scope for the application of existing models. It also leads to the development of new models that would otherwise be impractical. The balance of the course will take a look at some of these new models, with an emphasis on mixture modelling for the purpose of decision-making. Using BACC, we will use these models in two examples: education policy and financial risk management.

Intended results: At the end of this course, the participants will be able to combine the Bayesian analytical framework and Monte Carlo methods to construct econometric models to support decision-making.

Lecturer:

Prof. John Geweke is an expert in Bayesian Econometrics and a gifted teacher of theoretical and applied methods. He has the Harlan McGregor Chair at the University of Iowa. He is Co-Editor of the Journal of Econometrics, former president of the International Society for Bayesian Analysis, an elected Fellow of the Econometric Society and the American Statistical Association and has published over 100 research papers, many dealing with Bayesian econometrics. In 2005 he published the book Contemporary Bayesian Econometrics and Statistics that appeared in the Wiley Series in Probability and Statistics.

Target Group: PhD students, postdocs and university faculty

Course duration: 7 full days. Lectures on theoretical background in mornings and computer-assisted problem solving in the afternoons

Group size: Minimum 10 participants, maximum 20 participants.

(The organisers may cancel the course 3 weeks in advance in case the number of registrations did not reach the minimum).

Language: English

Location: Wageningen University, Leeuwenborch, Hollandseweg 1, Wageningen

Room Schedule:

Programme

Lectures/theory during the morning session and ‘hands on’ applications during the afternoon.

Morning sessions are from 09.00 – 12.00. Afternoon sessions from 13.30-16.00.

Meeting time Topic or nature of session Reading material

June 19 am Overview of Bayesian methods Chapter 1

June 19 pm Problem-solving session Exercises 1.2.1, 1.3.2, 1.3.3

June 20 am The linear and Markov chain models Sections 2.1, 6.3, 7.2

June 20 pm Problem-solving session Exercises 2.1.2, 2.1.4, 6.3.2

June 21 am Posterior simulation methods Sections 4.1-4.3

June 21 pm Orientation to computation Section 5.1, BACC manual

Example 5.1, Exercise 5.1.1

June 22 am Conjugate priors; decision theory; Sections 2.3, 2.4, 2.6

model comparison

June 22 pm Computation and decision-making Example 5.2, Exercises 5.1.2, 5.1.4

June 23 am Latent variables and mixture modeling Sections 6.1, 6.2, 6.4

June 23 pm Inference in mixture models Example 6.4.1, Exercise 6.4.4

June 26 am Models for time series Sections 7.1, 7.3

June 26 pm Applying the Markov normal mixture Examples 7.3.1, 7.3.2

model

June 27 am The smoothly mixing regression model Article reprint

June 27 pm Modeling financial data Exercises 7.3.1, 7.3.3

Prerequisite courses and recommended readings:

Students should have had at least one year of graduate level econometrics and have facility with linear algebra. The text for the course is Geweke, J. (2005) Contemporary Bayesian Econometrics and Statistics, Wiley. Participants should make sure they have this book before the course starts (book not included in participation fee). The first chapter of this book provides an overview of the course and should be read before attending the first meeting. The “hands on part” of the course will use the Bayesian Analysis Computation, and Communication software described in the text.

Credits and Examination:

This is a 4-ECTS credit course, which will be finished by a short paper (about 10-12 pages) that later can be transferred into a chapter in the dissertation. Attendance and active participation to the course and the completion of the short paper will be the conditions for credits. The paper should be handed in within six months and will be graded.

Course fee:

For PhD students of Mansholt Graduate School with an approved TSP the course fee is to € 300,-

For other participants the course fee is € 550. The course fee includes additional study and training materials, coffee / tea, lunches and workshop dinner. Note that the book of Geweke is not included!

Registration Procedure:

Register via the website

http://www.sls.wau.nl/mi/mgs/procedures_and_forms/Course_registration_form.htm

Deadline for registration is May 1, 2006. Please make sure you provide the most recent contact details so that in case of any changes you will be notified promptly. After your internet registration you will receive a short notification that your name has been registered. At least 2 weeks before the course you will receive a confirmation about the location and the schedule. MGS will also send a bill to your address indicated in the registration form.

Please e-mail to Marcella.haan@wur.nl in case you have not received the second confirmation two weeks before the course.

Cancellations:

The participants can cancel their registration without any fee 1 month before the course starts. Cancellation fee of 100% applies if participant cancels the course less than 1 month prior to the course.

The organisers have a right to cancel the course not later than 1 month before the course starts in case the number of registrations did not reach the minimum.

The participants will be notified of any changes at their e-mail addresses.

Further Information

For further information about the content of the course please contact the organiser:

Dr.ir. C. Gardebroek, Wageningen University, Hollandseweg 1, 6706 KN Wageningen; Tel. 0317 –482951; e-mail: Koos.Gardebroek@WUR.NL

For details about the logistics, accommodation, registration, fees, study materials, etc. please contact

Marcella Haan

Tel +31 317 484126

Marcella.haan@wur.nl

Further information on Mansholt Graduate School and its educational activities: http://www.sls.wau.nl/mi/mgs/courses/index.htm