統計計算
授課教師：陳宏老師（Email: HCHEN@MATH.NTU.EDU.TW，2363-3860轉109。舊數館106室）
上課時間及地點： 週三上午9:10-12:00，新生大樓104教室
諮詢時間：
週三8:30-9:00，12:00-12:30或以email約定時間
Prerequisite: One year graduate level mathematical statistics courses at the level of Casella and Berger's book entitled Statistical Inference.
| February | 18 | Introduction; statistical computing
in practice
EM algorithm Notes: [ content.pdf ] |
| February | 24 | R (in
brief)
Random number generation I Notes: montecarlo0.pdf Problem set: hw1.pdf Reading: R-intro.pdf |
| March | 3 | Random number generation
II Notes: montecarlo1.pdf Reading: |
| 10 | Numerical integration, Markov chain
Monte Carlo Notes: montecarlo2.pdf Problem set: hw2.pdf Reading: , Efron and Tibshirani (§ 9.5) | |
| 17 | 林宜靜博士演講 ”？” Monte Carlo Study, Resampling Methods: Permutation,
cross validation, and the bootstrap | |
| 24 | Resampling Methods; Linear Regression and numerical linear algebra
Notes: Problem set: hw3.pdf Reading: Thisted (ch 3) | |
| 31 | Linear Regression and numerical linear algebra Notes: Reading: | |
| April | 7 | Notes: Nonlinear regression and iteratively reweighted least
squares
Problem set: hw4.pdf
Reading: |
| 14 | Notes: Newton-Raphson, Fisher
scoring, Nonlinear regression[ pdf
(269k) ] Reading: | |
| 21 | EM algorithm extensions | |
| 28 | Downhill simplex method,
Lp regression and constrained optimization
Notes: Problem set: hw5.pdf Reading: | |
| May | 5 | Hidden Markov models Notes: Reading: |
| 12 | Notes: Problem set: hw6.pdf | |
| 19 | Notes: Reading: | |
| 26 | Problem set: hw7.pdf |
| June | 2 | Project presentation |
| 9 | Project presentation |
Bootstrap, Cross-Validation
Maximum Likelihood, EM algorithm, Missing
Data,
Step by step multivariate regression, robust
regression,
Non-parametric Regression, Alternate Conditional Expectation,
Projection Pursuit,
(Neural Nets)
Principal Components, Correspondence
Analysis,
Classification and Regression Trees, Clustering,
Multiple
response methods :PC-Instrumental Variables, Partial Least Squares,
Non
parametric methods for Longitudinal Matrices, Conjoint
Analysis,
Nonparametric Confidence Regions, (convex hulls),
Approximate
Counting, Exhaustive Enumeration, Non parametric Tests.
2. Algorithms
- The linear equation solving problem:
- Matrix manipulations, decompositions, (cholesky, QR,...),
- Singular Value Decompositions, Eigenanalysis,
- Iterative methods, Gauss-Seidel, Conjugate Gradient,
- Downhill Simplex minimization,
- Smoothing,
- Random Number Generation ,
(Uniform, Normal, Beta, Inverse CDF, Acceptance Rejection, Metropolis),- Markov Chain approach to Combinatorial Optimization (Simulated Annealing), Updating,
- Markov Chain Monte Carlo, Sorting.
3. Software
- Gentle, James E.: Numerical Linear Algebra for Applications in Statistics, Springer, New York(1998)
- Gentle, James E.: Random Number Generation and Monte Carlo Methods, Springer, New York(1998)
- Thisted, Ronald A.: Elements of Statistical Computing, Chapman and Hall, New York (1988)
Random Number Generators
George Marsaglia's "Mother of all RNGs" (C code with comments)
Overview of Random Number Generators in Cryptography
Example of a Cryptographic Random Number Generator
Refer to webpage of Computational Statistics taught by Prof. Gentle at George
Mason University on Students' class project
http://science.gmu.edu/$\sim$jgentle/csi771/02f/
（可由網路取得）at
Download at http://cran.r-project.org/
Look for base in Windows (95 and later)
Download rw1081.exe
R manuals: They are downloadable as PDF files: