STAT 680: Advanced Statistical Computing

Class meets: TR 9:20-10:50 am in: 1160 Sweeney
(see note at end of page)

Instructor: Ranjan Maitra (Ron-jone Moi-tro)

Office:2220 Snedecor Hall

Phone: (515)-294-7757

E-mail:maitra

Office Hours: T 2:10-3:00 pm, R 11:00-11:50 am, or by appointment.

Course Prerequisites:

Good knowledge of Stat 579, Stat 580 or permission of instructor
Excellent grounding in Stat 543
(Desired) knowledge of R or low-level programming language such as C.

Grading Scheme:

Homeworks: 50%

Projects and Presentation (Oral/Written): 50%

Course Description: This course is designed for Ph. D.-level students. It is designed to survey several computer-intensive methods in statistical inference. Because of the wide range of topics to be covered, there is no prescribed text-book for the class. I will try to provide a comprehensive set of notes. While the course is geared towards statistical computation, we will also look into the theory behind these methods. The broad outline for this course is as follows:

Review of Simulation: Brief review of methods for sampling from given distributions: direct methods, rejection sampling, adaptive rejection. Variance-reduction methods in simulation, importance sampling and use of antithetic variates.
Expectation-Maximization Algorithm and MC-EM: Theory behind Expectation-Maximization algorithm, EM in exponential families. Variance estimation for E-M. Methods for speeding up EM. Monte Carlo-EM: Applications to medical image analysis and/or statistical genetics
Randomization tests and the Bootstrap: Idea and techniques of Randomization tests; permutation tests, reference distributions, re-sampling methods such as jackknife and bootstrap. Parametric and non-parametric bootstrap. Estimation, confidence intervals and hypothesis testing.
Markov Chain Monte Carlo: Markov Chains and Markov Random Fields; use of Markov Random Field priors in Bayesian Inference and Markov Chain Monte Carlo Methods; Gibbs sampling, burn-in, exact simulation; Multi-grid methods. Applications to Spatial Models and Image Analysis

Homeworks:Homeworks will be handed out and due bi- or tri-weekly. These will consist of proving results and applying and exploring concepts learnt in class. A considerable part of the homework will involve computer work. All homework turned in must be professionally presented.

Projects: There will be one very substantive final project project assigned to each person during the semester. This project will involve either doing some exploratory work on a research problem, including detailed background literature study and analysis, etc or the statistical analysis of some appropriate dataset that you are interested in. You are welcome to provide this dataset in consultation with me. Another possibility would be some methodological investigation into some aspect of the topics covered n the class, or some investigation into, for instance, an engineering design problem, where the methods covered may be used to answer a question quantitatively. The final project will culminate in a written report and an oral presentation on the level of that for a professional meeting in statistics and its applied disciplines. For advanced Ph. D. students, an appropriately chosen project may serve as a portion of your dissertation. Each report will be graded on the validity of the statistical analysis, the scientific component, and the quality of the write-up and presentation in communicating the results to an intended professional audience.. You are required to electronically provide me with all written code, documentation and datasets used in the project. Your rights, if any, to the data and software, will be preserved.

Statistical Software: There is no requirement for this class, however knowledge of R will be assumed. Familiarity with a low-level programming language such as C will be helpful, but lack of it will not be a hindrance. Please note that this is NOT a class in learning statistical software. As such, you are welcome to use other software packages as long as it is able to meet your requirements.

Other: The times of the class may be adjusted to meet student requests and preferences. Further, to allow sufficient time for work on the final project, the lectures will be mostly concentrated in the first half of the semester: each class period will be lengthened to 1.8 credit hours.

Course Homepage: The course homepage will be located on the WWW at http://www.maitra.public.iastate.edu/stat680/fall2011.html. I will try and keep this homepage as upto date as possible. However, you are still responsible for any announcements made in class.