MODELING AND ANALYSIS
USING MONTE CARLO METHODS

A SHORT COURSE WITH GEORGE CASELLA

APRIL 24 and 25, 2008
GAINESVILLE, FLORIDA

Course Description

Monte Carlo statistical methods, particularly those based on Markov chains, have now matured to be part of the standard set of techniques used by statisticians. This short course is intended to serve as an introduction to both the application and underlying workings of these techniques, and to illustrate how Monte Carlo methods can enhance statistical practice through illustrations of the application of simulation based techniques to applied statistical problems.

The course will begin with the basics of random number generation and illustration of how a simulation approach can often supply easy methods for solving difficult problems. We will explore techniques for Monte Carlo integration and optimization, and then continue with the more recent Markov chain Monte Carlo techniques such as the Gibbs sampler and the Metropolis-Hastings Algorithm. We will use examples from life sciences, engineering, biostatistics, and many more. We will also have a detailed treatment of missing data models and analyses, with algorithms such as EM and Data Augmentation, and again provide examples and analyses from a variety of applications.

We strongly urge each student to bring a laptop computer that has a copy of both R and WinBUGS installed on it. There will be a number of examples worked out. WinBUGS is available free of charge, and can be downloaded from http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml. “R” is also free, available at  http://www.r-project.org/.

We will use examples both from Monte Carlo Statistical Methods, Second Edition,  by Robert and Casella (Springer-Verlag 2004) and other real life sources.

There is no required text for the course. Copies of all course slides and example output discussed will be provided.

Main topics covered are:

1.
 Introduction to random variable generation
2.
 Monte Carlo techniques for integration and optimization
3.
 The basics of Markov chain Monte Carlo
4.
 Modeling data in a hierarchy
5.
 Applications of Gibbs sampling and the Metropolis-Hastings Algorithm
6.
 Diagnosing the fit of the model

Who should Come?

We do not assume that the student has any familiarity with Monte Carlo techniques (such as random variable generation), or with any Markov chain theory. We do assume that the reader has familiarity with basic theoretical statistical concepts such as densities, distributions, probability and expectations, the Law of Large Numbers and the Central Limit Theorem, and maximum likelihood estimation. Hierarchical models are often analyzed using Bayesian methods. Familiarity with these methods is desirable but not essential, as the basics will be covered.

Some necessary background can be gained from the text Statistical Inference by Casella and Berger (Duxbury 2001), and much of the course related material will be based on the text Monte Carlo Statistical Methods .
The Instructor

George Casella is Distinguished Professor of Statistics at the University of Florida. He is active in many aspects of statistics including decision theory, statistical confidence, environmental statistics, statistical genomics and the theory and application of Monte Carlo and other computationally-intensive methods. He is a Fellow of the ASA and the Institute of Mathematical Statistics (IMS), has served as Theory and Methods Editor of JASA, Executive Editor of Statistical Science, and is currently Joint Editor of the Journal of the Royal Statistical Society, Series B.  He has authored six textbooks:

Statistical Inference, Second Edition, (2001), with Roger Berger

Variance Components, (1992), with S. R. Searle and C. E. McCulloch

Theory of Point Estimation, Second Edition, (1998), with Erich Lehmann

Monte Carlo Statistical Methods, Second Edition (2004), with Christian Robert

Statistical Genomics of Complex Traits (2007), with R. Wu and C. X. Ma

Statistical Design (2008)
Casella
Course Registration

To register for the short course please go to: registration form. Registration form must be printed and mailed along with your payment in the form of a check only.

Enrollment is restricted to the first 30 registrants. The course registration is $500 on or before April 10, 2008, and $575 after April 10, 2008.
Date and Location

The workshop will be held April 24-25, 2008  in Little Hall, Room 113 on the main campus.

The workshop will begin Thursday, April 24th at 9:00 AM and end at 4:30 PM.
Friday, April 25th the workshop will begin at 9:00 AM and end at 12:00 PM.

Additional Information

If you have additional questions about course content, please contact George Casella (casella@stat.ufl.edu). For questions about course logistics, please contact Carol Rozear (carol@stat.ufl.edu) or Robyn Crawford (robyn@stat.ufl.edu).