SATAISTICAL
COMPUTING
SPRING 2013
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Instructor: |
Guan-Hua Huang, Ph.D. |
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Office: 423 Joint Education Hall |
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Phone: 03-513-1334 |
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Email: ghuang@stat.nctu.edu.tw |
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Class meetings: |
Tuesday 9:00-12:00 at 407 Joint Education Hall |
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Office hours: |
By
appointment |
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Class website: |
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Credit: |
Three (3) credits |
COURSE
SUMMARY
This course will introduce topics in numerical
analysis useful for statistical modeling and analysis. Topics include computer programming,
random number generation, Monte Carlo simulation, permutation test and the
bootstrap, numerical linear algebra, the EM algorithm, optimization, numerical integration,
hidden Markov models, and Markov chain Monte Carlo.
HANDOUTS
AND TEXTBOOKS
Handouts corresponding to each lecture
will be available on the class website before each class. Reading assignments are from the following two books:
Ÿ
Lange K (2010). Numerical
Analysis for Statisticians, 2nd edition. Springer.
Ÿ
Venables WN and Ripley BD (2002). Modern
Applied Statistics with S, 4th edition. Springer.
PREREQUISITES
Students are
expected to have background on undergraduate probability, and mathematical
statistics. Computer programming knowledge on R/S-Plus/Matlab and/or C/C++ is
required.
METHOD
OF STUDENT EVALUATION
The course grade will be based on four to five homework assignments (50%), one midterm
exam (20%),
and one final exam (30%).
COURSE OUTLINE
Lange K
(2010). Numerical Analysis for Statisticians, 2nd edition.
Springer. (NAS)
Venables WN and Ripley BD (2002). Modern Applied Statistics with S, 4th edition. Springer. (MASS)
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Module |
Topic |
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1 |
Introduction;
R |
MASS Chapters 1-4 The R
manuals: |
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2 |
Linux;
LaTeX |
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3 |
Random
number generation |
NAS Chapter 22 MASS Section 5.2 |
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4 |
Permutation
test and the bootstrap |
NAS Chapter 24 |
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5 |
Numerical
linear algebra |
NAS Chapters 8-9 |
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6 |
EM
algorithm |
NAS Chapter 13 |
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7 |
Optimization:
Newton-Raphson, Fisher scoring |
NAS Chapter 14 |
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8 |
Nonlinear
regression, iteratively reweighted least squares |
NAS Sections 14.6 and 14.7 |
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9 |
EM
algorithm extensions |
NAS Chapter 13 |
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10 |
Lp
regression and constrained optimization |
NAS Chapter 11 |
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11 |
Numerical
integration |
NAS Chapter 18 |
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12 |
Hidden
Markov models |
NAS Section 25.3 |
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13 |
Markov
chain Monte Carlo I |
NAS Chapter 26 |
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14 |
Markov
chain Monte Carlo II |
NAS Chapter 27 |