Modeling and Analysis using Monte Carlo Methods – A Short Course
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 ontinue 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.
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, and
Registration
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.
Registration may be completed by contacting Robyn Crawford by e-mail
at
robyn@stat.ufl.edu or phone at 352.392.1941, ext 218.
Date and Location The workshop will be held April 24-25, 2008. The location on the UF campus will be announced soon.
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).
