jgentle@gmu.edu

This course is about modern, computationally-intensive methods in statistics. It emphasizes the role of computation as a fundamental tool of discovery in data analysis, of statistical inference, and for development of statistical theory and methods.

The text for the course is Elements of Computational Statistics.

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

Monte Carlo studies in statistics.

Brief introduction to random number generation.

Simulation of stochastic data generating processes in R or S-Plus.

**Assignment:** Read Section 2.1 (pages 39-53) and Appendix A and B
(pages 337-362).

Make a web page for your project.
Choose two articles in statistics literature that report Monte Carlo studies
and write brief descriptions of them on your web page.

Two examples from the March 2005 issue of the Journal of the American Statistical Association are the one by Romano and Wolf on problems of multiple hypothesis testing and the one by Lahiri and Larsen on regression with linked data. There are several more articles in that issue that use Monte Carlo simulation to study statistical methods.

You can use articles from any peer-reviewed scientific journal. Many are
available online; for example, the Journal of the
American Statistical Association is available by going the GMU
library home page, then to E-Journal Finder, then enter "American
Statistical Association" in the "keyword" box. Several options come up
next. The first one, "ABI/INFORM Complete", works.
*(Thanks to Pragyansmita Nayak for pointing this out!)*

Discussion of methods of 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 1.2, 1.3, 1.7, and 1.9 to
turn in (as hardcopies), Sept 19.

Comments/solutions.

Put a brief description of your project on your web page. You will
add to this description as the semester progresses.

Continue discussion of some material from Chapter 1 on least squares, and methods of optimization.

EM examples.

Random number generation; methods to convert uniform variates to other random variables (inverse CDF; acceptance/rejection).

**Assignment:** Read Chapter 2; work problems 2.2, 2.4, and 2.7 to
turn in, Sept 26.

Comments/solutions.

Review acceptance/rejection, Markov chain methods.

Inference using Monte Carlo: Monte Carlo tests, and "parametric bootstrap".

**Assignments:** Work problems 2.8 **note typo in solution on p. 379**,
2.9, and 2.10 to
turn in, Oct 3. Read Chapter 3.

Comments/solutions.

Randomization and data partitioning.

Bootstrap methods.

Outline.

Comments/solutions.

Transformations..

Outline.

Comments/solutions.

This will be open book and open notes.

Estimation of functions.

Comments/solutions.

k_{rs} = r/(2B(s+1,1/r))

A better way of writing the value is to use B(1/r,s+1) because that is the most obvious integral you see when you rewrite it. Of course, B(1/r,s+1)=B(s+1,1/r), so it doesn't matter.

**Assignments:** Read Chapter 9; work problems
9.3, 9.5, 9.10, 9.11 to turn in (due Nov 14 ** can turn in Nov 21**).

Comments/solutions.

More on nonparametric estimation of probability density functions.

Models of dependencies.

More on classification. Review.

Handout take-home portion of final exam.

This will be closed book and closed notes.

Another important repository for scientific computing is Netlib.