Welcome to CSI 779 / STAT 789

Topics in Computational Statistics:

Monte Carlo Methods

Spring, 1999

Instructor: James Gentle

Grading

Performance in the class will be evaluated based on

  • an in-class midterm (25%)
  • a final exam consisting of a take-home portion and an in-class portion (35%)
  • a project (30%)
  • a number of smaller assignments (10%)

    Each student will prepare a Web page for presentation of the project and for some of the smaller assignments.

    Texts and References

    There is no text for the course. Notes developed by the instructor will be given out from time to time, and some will be put on the net. The following references may be useful for supplementary study.

    Fishman, George S. (1996), Monte Carlo: Concepts, Algorithms, and Applications, Springer, New York.

    Gamerman, Dani (1997), Markov Chain Monte Carlo, Chapman & Hall, London.

    Gentle, James E. (1998), Random Number Generation and Monte Carlo Methods, Springer, New York.

    Knuth, Donald E. (1998), The Art of Computer Programming, Volume 2, Seminumerical Algorithms, third edition, Addison-Wesley Publishing Company, Reading Massachusetts.

    Krause, Andreas, and Melvin Olson (1997), The Basics of S and S-Plus, Springer, New York.

    Links to some useful Web sites will also be provided.

    For the project, it will be necessary to have access to statistical research journals. The Journal of the American Statistical Association, available in Fenwick Library and other places, is sufficient for this purpose.

    Topics and Schedule

    The planned weekly topics are shown below. There will likely be some deviations in the schedule, based on needs to spend more or less time on individual topics.

    January 27

    Introduction to local computing facilities; Web page construction.
    Monte Carlo studies in statistics.
    Generation of random numbers from a uniform distribution
    Monte Carlo quadrature
    Basics of S-Plus

    February 3

    Generation of random numbers from non-uniform distributions
    Student descriptions of Monte Carlo studies in literature.
  • Project milestone: Student reports on two articles in statistics literature that report Monte Carlo studies. (Reports should be about 10 minutes)

    February 10

    Generation of random numbers from non-uniform distributions (continued)
    Monte Carlo quadrature (continued)
    Variance reduction
  • Project milestone: Design a plan to replicate and extend one of the studies. (No reports, but class time will be available for questions or discussions.)

    February 17

    Testing random number generators
    Quasirandom sequences
    Assignment
  • Project milestone: Student reports of feasibility study (software, etc.). (Reports should be about 10 minutes)

    February 24

    Increasing efficiency of Monte Carlo

    February 27

    Variance reduction (continued)

    March 3

    Statistical inference using Monte Carlo
    Monte Carlo tests, Monte Carlo bootstrap, Monte Carlo quadrature

    March 10

  • Midterm exam (in class)

    March 17

    No class.

    March 24

    Random walks and Markov processes

    March 31

    No lecture.
  • Project milestone: Student reports of Monte Carlo study.

    April 7

    Markov chain Monte Carlo
    Metropolis methods and variations

    April 14

    No lecture.
  • Project milestone: Presentation and discussion of project reviews (by the reviewer)

    April 21

    Bayesian methods of analysis
    Markov chain Monte Carlo applications

    April 28

    No lecture.
  • Project milestone: Final presentations of projects.

    May 5

    Markov chain Monte Carlo applications (continued)
    Distribution of take-home portion of final exam.

    May 12

    In-class portion of final exam

    Resources

    Labs with Unix workstations are available for use in this class in both CSI and IT&E.
  • CSI facilities.
  • Software available in SITE labs.

    The most important WWW repository of statistical stuff (datasets, programs, general information, connection to other sites, etc.) is StatLib Index at Carnegie Mellon.

    James Gentle, jgentle@gmu.edu