Welcome to CSI 771 / STAT 751

Computational Statistics

Fall, 2009

Instructor: James Gentle

Lectures: Thursday, 4:30-7:10pm, Engineering Building, room 1108

Some of the lectures will be based on notes posted on this website. Some lectures will be accompanied only by notes written on the board.

If you send email to the instructor, please put "CSI 771" or "STAT 751" in the subject line.

The general description of the course is available at mason.gmu.edu/~jgentle/csi771/

Prerequisites:

  • a course in applied statistics such as STAT 554
  • a course in statistical inference such as CSI 672 / STAT 652.

    Text: Computational Statistics ISBN 978-0-387-98143-7.
    We will cover most of Parts I, III, and IV.

    Software: The main computational software is R.

    R is open source and is free. It is installed on some GMU computers, but there are various binary executables available at the main R website, and it is best to load it on your own computer.

    A good way to learn R is just to use it for progressively more complicated problems. While there are many books on R, the various pdf manuals that come with the installation (use "Help" on the GUI) should be sufficient.

    Grading

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

    Project:
    The course requires each student to complete a project that involves a Monte Carlo study of a statistical method.

    Collaboration and Academic Integrity
    Each student enrolled in this course must assume the responsibilities of an active participant in GMU's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. The GMU policy on academic conduct will be followed in this course.

    Group work and discussion outside of class is encouraged, but of course explicit copying of homework solutions should not be done.

    For in-class exams, one sheet of notes will be allowed. The preparation of that sheet is one of the most important learning activities.

    Lectures / assignments / exams schedule

    Week 1, September 3
    General introduction; Appendix A; R

    Monte Carlo methods in statistics.

    Brief introduction to R.
    R functions.
    Random number generation in R.

    Saving graphics files in R.

    Assignments: Read Appendix A (page 643); work problem 1.18 (page 77) to turn in (in hardcopy on September 10).

    Week 2, September 10
    Chapter 1

    Graphical displays.

    Statistical inference.
    The role of optimization in statistical estimation: minimization of residuals; maximization of likelihood; etc.
    The functional approach to statistical estimation.

    Assignments: Read Chapter 1; work problems 1.15, 1.16, and 1.21 to turn in (in hardcopy on September 17).

    Week 3, September 17
    Chapter 9; review Section 1.2; parts of Chapter 5

    Norms of matrices; condition measures.
    Linear transformations.
    Measures of similarity.

    Matrices in R.

    Geometry in R.

    Assignments: Read Chapter 9; work problems 1.5, 5.1, 9.1, 9.2, and 9.13 to turn in (in hardcopy on September 24).

    Week 4, September 24
    Chapter 10; parts of Chapter 4

    Estimation of functions.

    Assignments: Read Chapter 10; work problems 10.1, 10.3, and 10.4 to turn in (in hardcopy on October 1).

    Week 5, October 1
    Begin Chapter 11; review Appendix A

    Monte Carlo methods of inference.

    Week 6, October 8

    Midterm exam. Closed book and closed notes except for one sheet (front and back) of prewritten notes.
    Sample from a previous year.

    Week 7, October 15
    Chapter 11; Chapter 12

    Review midterm.

    Discuss semester project (Exercises A.2 and A.3)

    Monte Carlo methods of inference

    Assignment: Exercise A.2, with just 2 articles, and can be some other statistical journal.

    Week 8, October 22
    Chapter 7, Chapter 12

    Student reports on plans for projects.

    Methods of transforming uniform random variables to random variables from other distributions.

    Data partitioning; jackknife methods.

    Assignment: Work problems 7.2, 11.3, 11.7, 12.1, and 12.6 to turn in (in hardcopy on October 29).

    Week 9, October 29
    Chapter 13

    Bootstrap methods.
    Additional reference: Maria L. Rizzo (2007) Statistical Computing with R
    Also see R programs at author's website.

    Assignment: Work problems 13.1, 13.2, and 13.8 to turn in (in hardcopy on November 5).

    Week 10, November 5
    Chapter 14; Cahpter 15

    Probability density estimation.

    Assignment: Work problems 14.1, 14.2, and 15.1 to turn in (in hardcopy on November 12).

    Week 11, November 12
    Chapter 15, Chapter 16

    Nonparametric probability density estimation.
    Statistical learning.

    Assignment: Work problems 15.2 a) and b), 15.11, 15.13, and 16.1 to turn in (in hardcopy on November 19).
    Solutions; comments.

    Week 12, November 19
    Chapter 16


    Statistical learning: ordering multivariate data; principal components; projection pursuit. We did not have time to discuss projection pursuit, so it will not be considered to be part of the course.

    Assignment: Work problems 16.5 and 16.7 a) to turn in (in hardcopy on December 3) and work problem 16.8 not to turn in.
    Solutions; comments.

    November 26

    Class does not meet this week

    Week 13, December 3

    Presentations of projects.

    Assignment: Work problem 16.6 (not to turn in).

    Week 14, December 10
    Chapter 17

    Models of dependencies, other topics, or review, as necessary.

    December 17

    4:30pm - 7:15pm Final Exam.
    Closed book and closed notes except for one sheet of prewritten notes.