STA 590 STATISTICAL COMPUTING


Department of Mathematics and Statistics, UNM


Spring Semester 2005


INSTRUCTOR

Dr. Gabriel Huerta
Office: 441 Humanities Building
email: ghuerta at stat.unm.edu
Class Time: Tue. and Thurs. 2:00-3:15pm.
Classroom: 334 Dane Smith Hall
Course Web-Page: http://www.stat.unm.edu/~ghuerta/sta590/course.html
Office Hours: Tue. and Thurs. 3:30-5:15pm or by appointment.
*Please send me a note by e-mail to make an appointment outside office hours.


HANDOUTS AND CODE

  • Class Jan 20 ; Code Jan 20 .
  • Class Jan 25 ; Code Class Jan 25
  • Class Feb 1 ; Code Class Feb 1
  • Slides Class Feb 15-17 ; Code Class Feb 15-17
  • Normalized likelihood for Genetic Link Example
  • Slides Class Feb. 24; Code Class Feb.24
  • Bivariate Normal Example
  • Slides Class Mar. 02; Code Class Mar. 02
  • Speed of Light example; R Code
  • Data Augmentation Example.
  • M-H Examples. Slides Class Mar. 24
  • Notes about the BOA routines
  • Slides Class Apr. 14
  • Fortran Files: More examples ; Simulation of RVs ; M-H Example ; Fortran 77 routines.
  • Slides about BUGS
  • Class on Extreme Values ; R code

    • HOMEWORK

  • HW # 1. Tanner's book. Chapter 2 Exercises 1, 5 and 8. Due Jan. 27.
  • HW # 2 Tanner's book. Chapter 1 Exercises 1,3, 5. Chapter 2 Exercises 9, 10. Due Feb. 10. Attend Steve Fienberg's seminar on Feb. 10.
  • HW # 3 Tanner's book Chapter 3 , Exercises 2, 3 (a and b only), 6 and 7. Due March 1.
  • HW # 4 pdf file
  • HW # 5 pdf file
  • HW # 6 Tanner's book page 86. Exercise 1 parts a),b) and d). Exercise 2 page 86. Due on April 21.
  • HW # 7 For the Genetic Linkeage Example make a Fortran 90 implementation of the Newton-Rapshon algorithm (exercise 9 HW#2). Due the last of class.
    DESCRIPTION

    This course is concerned with advanced statistical modeling and modern methods of computation to solve integration and approximation problems for statistical inference. The main topics to be covered are Normal approximations, Monte Carlo methods, E-M/data augmentation algorithms and Markov Chain Monte Carlo (MCMC) methods. Applications and data sets will be drawn from different sources including problems in time series, spatial analysis, ordinal data. The computations will be developed using software packages such as S-plus/R, Matlab, Bugs or Winbugs. This course will not cover any material on SAS. For that purpose, I recommend you take Stat 528.

    PREREQUISITES

    STA 453/553: Statistical Inference or permission of the instructor

    In order to have a complete understading of this course, you must have some familiarity with the main concepts of statistical inference for parametric models including, families of distribution functions, likelihood, Bayesian approach, point estimation and interval estimation. Some quick review of this concepts will be made during the first week of classes. I will assume that you have some familiarity with the use of the computer and computer software. The main goal of this course is that you are capable to understand and implement some of the techniques discussed in this class using the computer .

    TEXTBOOK

  • Tanner, M. A. (1996) Tools for Statistical Inference: Methods for the Exploration of Posterior Distribution, 3rd Ed. Springer Verlag: New York

    • ADDITIONAL REFERENCES

  • Gamerman, D. (1997) Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference Chapman and Hall.

  • Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1995) Markov Chain Monte Carlo in Practice. Chapman and Hall.

  • Maindonald, J. H. and Braun, J. (2003) Data analysis and graphics using R. Cambridge University Press.

    • These books are written at an introductory level and contain the core material that will be cover in the course. Since the amount of literature in the topic is abudant, further references will be given along the course.


    MAIN TOPICS

  • Review of likelihood inference and Bayesian modeling.
  • Introduction to R.
  • Generation of Random Quantities.
  • Normal approximations and Monte Carlo Integration
  • EM and Data Augmentation algorithms.
  • Gibbs Sampling and Metropolis-Hastings algorithms.
  • Introduction to Bugs/Winbugs
  • Advanced topics: Convergence, Hybrid methods, Reversible Jump.
  • Advanced topics: Bootstrap, Introduction to Fortran.
  • Examples in hierarchical modeling, time series, spatial analysis, ordinal data
    • GRADING

    The grading will be based on homework assignments and a final project. Homeworks will be assigned regularly (roughly every other week) and will involve 'theory' and 'computer' exercises. I expect homeworks to be presented in time and as neatly as you can, including all relevant information: graphs, detailed proofs,discussion on results, etc. The final project could take the form of an applied investigation making use of some of the techinques discussed in the course or a critical review of a suitable paper. The final project in the form of a short document will be due during the last week of classes. The final project may involve a short class presentation or some advanced programming in Fortran.

    SOFTWARE

    Here are some links to software material of relevance to the class. This information will be updated along the semester.

    FREE Splus, version for students.

    Splus, documentation with many examples of how to perform statistical analysis using Splus.

    The R software package.

    The BUGS project and the WinBUGS development web-site.

    The BOA program for MCMC convergence analysis.