Welcome to CSI 771

Computational Statistics

Instructor: James Gentle

Fall, 1996

Topics to be covered include

Basics of statistical computing

Monte Carlo studies in statistics

Random number generation and other applications

Nonparametric smoothing

Nonparametric probability density estimation

Data partitioning and resampling

PostScript versions of some of the lectures, ASCII files of data, and other files will be available online.

The text is Computational Statistics , Chapters 1, 2, 8, 9, and 10.
A preliminary version of the text is in the GMU Copy Center in the Johnson Learning Center.

Student work in the course (and the relative weighting of this work in the overall grade) will consist of

a number of small assignments, problems, etc. (15)

a semester project to replicate and extend a published Monte Carlo study (30)

an in-class midterm (25)

a final exam consisting of an in-class component and a take-home component (30)

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

August 28 Lecture 1:

Course overview; method of communication
Computer organization: Unix and basic tools; S-Plus
Computational statistics
Monte Carlo studies
Random number generation in S-Plus

September 4

More on Monte Carlo simulation
*Summaries of two articles due
5-minute presentations

September 11

Random number generation

September 18

Student presentations of project plans
Assignment: Read Section 1.2.1 and Section 2.1. Work exercises, Chapter 1, #15, Chapter 2, #2, #6, #8, #13

September 25

Random number generation from non-uniform distributions
Assignment: Read Sections 2.2, 2.3, and 2.4. Work exercises, Chapter 2, #16, #18, #20a, #24, #25, and this question:
Consider the problem of taking a simple random sample from a file containing 1,000,000 items. Suppose the sample size is 500. What is the order of magnitude of the cardinality of the sample space? (That is, how many different samples are possible?) What is the problem here? Suppose you are going to use a random number generator with period of the order of 10^9. What is the largest sample size you could take, and still satisfy the requirement that it be simple random sample? (In addressing this question, do not be concerned about any differences in pseudorandomness and randomness.)

October 2

Monte Carlo methods; quasirandom numbers.
Assignment: Read Sections 2.5, 2.6, and 2.7. Work exercises, Chapter 2, #26, #27, and this problem:
Write a code for RANDU, as in Exercise 4. Generate 1,002 deviates with it and put them in an S-Plus 1000 by 3 matrix such that the first column is x_1, x_2, ...., the second column is x_2, x_3, ....; and the third column is x_3, x_4, .... Now use the S-Plus function spin to spin a point cloud. Can you see the planes?

October 9 No Class

October 16

Bootstrap Methods

October 23

More on the bootstrap and Monte Carlo tests

October 30 In-class midterm (PostScript)

November 6

Review of midterm (PostScript)
Student presentations of reviews of Monte Carlo studies.

November 13

Data partitioning and resampling

November 20

Nonparametric probability density estimation

November 27

Nonparametric regression and other nonparametric smoothing

December 4

Student presentations of Monte Carlo studies.
Hand out take-home portion of final.
PostScript version
TeX version

December 11 Final

Computational Resources

Labs with Unix workstations are available for use in this class in both CSI and SITE.

CSI facilities.

Software available in SITE labs.

S (or S-Plus)

Cheatsheet (courtesy of Barry Brown, University of Texas at Houston)
S (or S-Plus) FAQ (courtesy of many people, primarily, currently, Charles Roosen)

Other Resources

It will be necessary to use Unix for assignments and the project, so some familiarity with it is necessary.

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

Students

The students in the class all have homepages on which they put parts of their assignments and other interesting stuff.

Ricardo Esquer-Blasco

Qi Zhu

James Gentle, jgentle@gmu.edu