Type of Credit: Required
Credit(s)
Number of Students
Mathematical analysis was used to be the most useful tool, and probably the only tool, in handling statistical problems. The rapid development of computers in recent years has made simulation a powerful tool as well, and it is especially convenient in dealing with problems without “good” statistical assumption. However, simulation is like mathematical experimentation, it needs careful design and planning in order to come out with satisfied results. At the first half of this course, we will introduce basic principles of computing and simulation, including generation of random numbers and random variables, and statistical tests.
能力項目說明
The goal of this course is to train students with the ability of basic computing and simulation. Advanced techniques and applications shall be covered in the second half of the semester. Topics covered in this course include: Simulation and Monte Carlo methods, Matrix computation, Numerical integration and approximation, Data partition and resampling, Optimization methods, Density estimation, and Bayesian computing. Also, the use of statistical software R/S-Plus is required in this course. The software R can be downloaded via http://www.r-project.org.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
The homework is usually on a 2-week interval base and due on Tuesday/ Friday afternoon at 5. However, you need to hand-in your homework and final report in hard copy, and no email copies are allowed.
Weekly Class Schedule:
1. Class Introduction (Week 1)
2. Simulation and Monte Carlo methods (Weeks 2~3), Homework #1
àPseudo-random number generation, Linear congruential method, Inverse method, Rejection method, and Statistical tests
3. Matrix computation (Weeks 4~5), Homework #2
àLeast square methods, Gram-Schmidt method, Gaussian elimination, Singular value decomposition, Cholesky decomposition
4. Numerical integration and approximation (Weeks 6~7)
àTrapezoidal and Simpson’s rules, General Newton-Cotes rules, Monte-Carlo integration
5. Data partition and resampling (Weeks 8~9), Homework #3
àBias reduction, Variance estimation using Jackknife and Bootstrap (including Dependent Data and Bootstrap), MCMC (Markov Chain Monte Carlo)
6. Optimization methods (Weeks 10~11), Homework #4
àMaximum likelihood estimation, Newton-Raphson and Newton like methods, Fisher scoring methods, EM algorithm
7. Density estimation (Weeks 12~13)
àHistograms and related density estimator, Spline smoothing, Kernel smoothing
8. Bayesian computing (Weeks 14~15), Homework #5
àBayes' Theorem, Bayesian thinking, Bayesian computation, Markov Chain Monte Carlo methods
9. Applications (Weeks 16~17)
Homework 45%
Class Participation 20%
Final Project 35%
Elements of Statistical Computing (1988) by R.A. Thisted
Modern Applied Statistics with S-Plus (1999) by W.N. Venables & B.D. Ripley
Numerical Methods of Statistics (2001) by J.F. Monahan
Handbook of Computational Statistics: Concepts and Methods (2004) by J. E. Gentle, W. Härdle, and Y. Mori (Eds.)
Stochastic Simulation (1987) by B.D. Ripley
A Course in Simulation (1990) by S.M. Ross
Modern Simulation and Modeling (1998) by R.Y. Rubinstein & B. Melamed
Simulation and the Monte Carlo Method (1981) by R.Y. Rubinstein
Manuals and References at www.r-project.org
my website http://csyue.nccu.edu.tw